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\303\247\303\265es Formais de s\303\251ries de EDOs
<Text-field style="Heading 1" layout="Heading 1"><Font encoding="UTF-8">Introdu\303\247\303\243o</Font></Text-field>Nesse artigo, examinaremos tanto como implementar os algoritmos de etapas cl\303\241ssicos, tal como obter seus resultados aplicando os mais poderosos comandos do Maple.
<Text-field style="Heading 1" layout="Heading 1"><Font encoding="UTF-8">Inicializa\303\247\303\265es</Font></Text-field>restart;with(Student[Calculus1]):
with(PDEtools):
<Text-field style="Heading 1" layout="Heading 1"><Font encoding="UTF-8">Implementando o Algoritmo Cl\303\241ssico no Maple</Font></Text-field>Considere a equa\303\247\303\243o diferencialde := 2*x*diff(y(x),x,x)+(1+x)*diff(y(x),x)-2*y(x);aparecendo na Se\303\247\303\243o 107, p\303\241ginas 317-20, no livro de Rainville Elementary Differential Equations. Em LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRIjBGJ0Y5Rjk=, o Maple fornecedsolve(de, y(x), formal_solution);como solu\303\247\303\243o geral. Mais tarde, mostraremos que o Maple pode fornecer a solu\303\247\303\243o em uma forma mais simples em que LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEkX24xRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnL0YzUSdub3JtYWxGJw== \303\251 substitu\303\255do pelo visualmente mais simples LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEibkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=.A solu\303\247\303\243o cl\303\241ssica dessa equa\303\247\303\243o come\303\247a com a determina\303\247\303\243o de seus pontos singulares. Obtemos esses com o comando do MapleDEtools[singularities](de);onde usamos os nomes longos para comandos nos pacotes DEtools, gfun, e Slode que cont\303\251m as ferramentas que necessitamos para nossas investiga\303\247\303\265es.O comando usado h\303\241 pouco nos diz que LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRIjBGJ0Y5Rjk= \303\251 um ponto regular singular, e que o ponto no infinito \303\251 um ponto singular irregular. Todos os outros pontos s\303\243o pontos regulares onde existem duas solu\303\247\303\265es convergentes da s\303\251rie de Taylor. No ponto regular singular, existe ao menos uma solu\303\247\303\243o da formaY := Sum(a[k]*x^(k+c),k=0..infinity);O resultado da substitui\303\247\303\243o dessa solu\303\247\303\243o formal na equa\303\247\303\243o diferencial requer diferentes manipula\303\247\303\265es em termos diferentes, e isso \303\251 dif\303\255cil de se fazer no Maple. \303\211 melhor trabalhar termo a termo na equa\303\247\303\243o diferencial. Para isso, primeiro obtemos (e simplificamos) a primeira e segunda derivadas da s\303\251rie formal.Y1 := combine(diff(Y,x));
Y2 := combine(diff(Y1,x));O grau do termo gen\303\251rico na segunda derivada foi baixado para 2, e na primeira derivada, para 1. Quando a segunda derivada \303\251 multiplicada por LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=, seu termo gen\303\251rico ser\303\241 compar\303\241vel ao da primeira derivada. Portanto, formamos e simplificamos a somaT1 := factor(combine(2*x*Y2 + Y1));Quando a primeira derivada \303\251 multiplicada por LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=, o termo gen\303\251rico ser\303\241 compar\303\241vel com ele mesmo em LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Ji1GLDYlUSJ5RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEwJkFwcGx5RnVuY3Rpb247RicvRjhRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZCLyUpc3RyZXRjaHlHRkIvJSpzeW1tZXRyaWNHRkIvJShsYXJnZW9wR0ZCLyUubW92YWJsZWxpbWl0c0dGQi8lJ2FjY2VudEdGQi8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRlEtSShtZmVuY2VkR0YkNiQtRiM2JC1GLDYlUSJ4RidGNEY3Rj5GPkY+RitGPg==, e assim formamos e simplificamos a somaT2 := factor(combine(x*Y1-2*Y));Para combin\303\241-los para somas formais, precisamos "baixar" o \303\255ndice na segunda soma. Fazemos isso no Maple comtemp := dchange(k=n-1,T2):
T3 := dchange(n=k,temp);Antes podemos adicionar a soma come\303\247ando em LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEia0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRIjBGJ0Y5Rjk= com a nova soma que come\303\247a com LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEia0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRIjFGJ0Y5Rjk=, precisamos extrair o termo LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEia0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRIjBGJ0Y5Rjk= da primeira soma. \303\211 melhor extrair o somat\303\263rio comS1 := Summand(T1)[1];avaliar esse somat\303\263rio em LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEia0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRIjBGJ0Y5Rjk= para terq := eval(S1,k=0);e ent\303\243o reconstruir a soma resultante comoT4 := Sum(S1,k=1..infinity);O termo extra\303\255do LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEia0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRIjBGJ0Y5Rjk= leva \303\240 equa\303\247\303\243o indicialIndicialEquation := remove(has,q,{x,a}) = 0;cujas ra\303\255zes s\303\243osolve(IndicialEquation,c);Desse modo, em um ponto singular regular LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRIjBGJ0Y5Rjk=, uma solu\303\247\303\243o ser\303\241 a s\303\251rie de Taylor, e a outra ser\303\241 uma s\303\251rie de Taylor multiplicada por LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictSSZtc3FydEdGJDYjLUYsNiVRInhGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRidGKy9GOVEnbm9ybWFsRic=.Para determinar o coeficiente geral em cada uma dessas s\303\251ries solu\303\247\303\243o, adicionamos e simplificamos as duas somas que agora possuem termos compar\303\241veis gen\303\251ricos e \303\255ndices iniciais id\303\252nticos. Portanto, obtemosT5 := factor(combine(T4+T3));O desaparecimento id\303\252ntico de cada coeficiente \303\251 assegurado por equacionar o coeficiente gen\303\251rico nessa soma por zero. Isolando LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictSSVtc3ViR0YkNiUtRiw2JVEiYUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GLDYlUSJrRidGNUY4LyUvc3Vic2NyaXB0c2hpZnRHUSIwRidGKy9GOVEnbm9ybWFsRic= leva \303\240 equa\303\247\303\243o recursivaRecursionEqn := factor(isolate(Summand(T5)[1]=0,a[k]));Sem alguns dos softwares ferramenta dispon\303\255veis, o estudante que resolve essa equa\303\247\303\243o recorrente deve considerar separadamente as duas recurs\303\265es correspondentes \303\240s duas ra\303\255zes indiciais, LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEiY0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRIjBGJ0Y5Rjk= e 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. Para cada, a recurs\303\243o \303\251 usada para gerar uma sequ\303\252ncia de termos dos quais um padr\303\243o geral deve ser deduzido. Em vez disso, exploraremos o uso do comando rsolve do Maple, o solucionador designado por equa\303\247\303\265es recursivas.Infelizmente, esse solucionador usa nota\303\247\303\243o de fun\303\247\303\243o, n\303\243o nota\303\247\303\243o subescrita, pelo que sabemos, Unfortunately, this solver uses function notation, not subscript notation, for the unknown. Portanto, escrevemosQ := eval(RecursionEqn, [a[k]=u(k), a[k-1]=u(k-1)]);Avaliando essa equa\303\247\303\243o para cada raiz indicial d\303\241 as recurs\303\265esQ0 := eval(Q, c=0);
Q1 := simplify(eval(Q, c=1/2));Essas solu\303\247\303\265es s\303\243o, respectivamente,U0 := rsolve(Q0, u(k)):
U1 := rsolve(Q1, u(k)):
u(k) = U0;
u(k) = U1;Uma inspe\303\247\303\243o cuidadosa dos primeiros resultados mostra que 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 Isso \303\251 claro de eval(U0, k=1);
eval(U0, k=2);
eval(U0, k=3);O segundo resultado gera os coeficientesfor n from 0 to 5 do
eval(U1, k=n);
end do;cujo padr\303\243o n\303\243o \303\251 imediatamente \303\263bvio. A Tabela 1 cont\303\251m as primeiras rela\303\247\303\265es individuais geradas pela recurs\303\243o.
for n from 1 to 6 do
eval(Q1, k=n);
end do;Tablela 1 Recurs\303\265es para 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
A tabela 1 mostra que LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Ji1GLDYlUSJ1RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEwJkFwcGx5RnVuY3Rpb247RicvRjhRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZCLyUpc3RyZXRjaHlHRkIvJSpzeW1tZXRyaWNHRkIvJShsYXJnZW9wR0ZCLyUubW92YWJsZWxpbWl0c0dGQi8lJ2FjY2VudEdGQi8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRlEtSShtZmVuY2VkR0YkNiQtRiM2JC1GLDYlUSJuRidGNEY3Rj5GPkY+RitGPg== \303\251 dado em termos de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Ji1GLDYlUSJ1RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEwJkFwcGx5RnVuY3Rpb247RicvRjhRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZCLyUpc3RyZXRjaHlHRkIvJSpzeW1tZXRyaWNHRkIvJShsYXJnZW9wR0ZCLyUubW92YWJsZWxpbWl0c0dGQi8lJ2FjY2VudEdGQi8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRlEtSShtZmVuY2VkR0YkNiQtRiM2JC1JI21uR0YkNiRRIjBGJ0Y+Rj5GPkY+RitGPg== como um produto dos fatores de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Ji1GLDYlUSJ1RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEwJkFwcGx5RnVuY3Rpb247RicvRjhRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZCLyUpc3RyZXRjaHlHRkIvJSpzeW1tZXRyaWNHRkIvJShsYXJnZW9wR0ZCLyUubW92YWJsZWxpbWl0c0dGQi8lJ2FjY2VudEdGQi8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRlEtSShtZmVuY2VkR0YkNiQtRiM2JC1GLDYlUSJrRidGNEY3Rj5GPkY+RitGPg== aparecendo no lado direito de cada uma das equa\303\247\303\265es exemplificadas na tabela. Portanto, LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Ji1GLDYlUSJ1RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEwJkFwcGx5RnVuY3Rpb247RicvRjhRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZCLyUpc3RyZXRjaHlHRkIvJSpzeW1tZXRyaWNHRkIvJShsYXJnZW9wR0ZCLyUubW92YWJsZWxpbWl0c0dGQi8lJ2FjY2VudEdGQi8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRlEtSShtZmVuY2VkR0YkNiQtRiM2JC1GLDYlUSJuRidGNEY3Rj5GPkY+RitGPg== poderia ser dado pelo produto dos fatoresP := coeff(rhs(Q1), u(k-1));isso \303\251, porunassign('n');
un := value(Product(P,k=1..n)):
u(n) = un;Desse modo, determinamos que a solu\303\247\303\243o geral da equa\303\247\303\243o diferencial \303\251 uma combina\303\247\303\243o linear de um polin\303\264mio finito (de fato, quadr\303\241tico) e uma s\303\251rie de Taylor multiplicada por LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictSSZtc3FydEdGJDYjLUYsNiVRInhGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRidGKy9GOVEnbm9ybWFsRic=.Uma s\303\251rie solu\303\247\303\243o completa mesmo uma equa\303\247\303\243o linear de segunda ordem claramente toma uma quantidade consider\303\241vel de habilidade manipuladora se a solu\303\247\303\243o for gerada manualmente usando algoritmos cl\303\241ssicos. Vamos ver como o Maple pode providenciar a solu\303\247\303\243o completa com o m\303\255nimo de esfor\303\247o da parte do usu\303\241rio.
<Text-field style="Heading 1" layout="Heading 1"><Font encoding="UTF-8">Solu\303\247\303\243o do Maple com M\303\255nimo de Esfor\303\247o</Font></Text-field>Dada a equa\303\247\303\243o diferencialde;mostramos como o Maple fornece os pontos singulares viaDEtools[singularities](de);No ponto regular singular LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRIjBGJ0Y5Rjk=, a equa\303\247\303\243o diferencial possui um conjunto fundamental consistindo de ao menos uma s\303\251rie da formaY;Para determinar os valores apropriados para o par\303\242metro LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiY0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=, temosDEtools[indicialeq](de, x, 0, y(x));a gera\303\247\303\243o autom\303\241tica da equa\303\247\303\243o indicial cujas ra\303\255zes s\303\243o claramente LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEiY0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRIjBGJ0Y5Rjk= e 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.Maple ainda classifica os pontos como hipergeom\303\251trico, racional, ou polinomial (respectivamente) com o comandoSlode[candidate_points](de, y(x));Pontos hipergeom\303\251tricos s\303\243o aqueles cujos coeficientes nas solu\303\247\303\265es s\303\251rie obedecem equa\303\247\303\265es lineares recursivas. Consequentemente, no ponto regular singular LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRIjBGJ0Y5Rjk=, um conjunto fundamental de solu\303\247\303\265es para a equa\303\247\303\243o diferencial pode ser gerado pelo comando do MapleFS := Slode[hypergeom_formal_sol](de, y(x));Desse modo, recuperamos todas as informa\303\247\303\265es da se\303\247\303\243o anterior, exeto pelas equa\303\247\303\265es recorrentes satisfeitas pelos coeficientes das s\303\251ries solu\303\247\303\243o. Antes de vermos como o Maple poderia nos fornecer essas recurs\303\265es, primeiro temos que ter certeza que a s\303\251rie solu\303\247\303\243o dada aqui concorda com os resultados das se\303\247\303\243o anterior onde encontramos o seguinte coeficiente geral un;(As solu\303\247\303\265es polinomiais s\303\243o claramente as mesmas.) Para come\303\247ar a compara\303\247\303\243o das duas s\303\251ries solu\303\247\303\243o, priemiro extra\303\255mosa nova solu\303\247\303\243o viaFS1 := select(has,FS,GAMMA)[1];e ent\303\243o selecionamos o somat\303\263rio comFS2 := Summand(FS1)[1];Infelezmente, essa express\303\243o cont\303\251m vari\303\241veis "locais" que modificamos comFS3 := convert(FS2,`global`);Uma vez que queremos comparar as express\303\265es para os coeficientes de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictSSVtc3VwR0YkNiUtRiw2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GLDYlUSJuRidGNUY4LyUxc3VwZXJzY3JpcHRzaGlmdEdRIjBGJ0YrL0Y5USdub3JtYWxGJw== nas duas vers\303\265es das s\303\251ries que geramos, escrevemosFS4 := remove(has,FS3,x^n);e comparamos via a raz\303\243osimplify(FS4/un);Portanto, as duas vers\303\265es das s\303\251ries solu\303\247\303\243o diferem por somente um m\303\272ltiplo constante, e ent\303\243o conclu\303\255mos que ambas as s\303\251ries solu\303\247\303\243o s\303\243o essencialmente as mesmas.O item final que o algoritmo cl\303\241ssico fornece \303\251 a rela\303\247\303\243o recorrente satisfeita pelos coeficientes nas s\303\251ries solu\303\247\303\243o. Os comandos do MapleR1 := gfun[diffeqtorec](de, y(x), u(n));
R2 := Slode[FPseries](de, y(x), u(n));ambos fornecem somente uma rela\303\247\303\243o recursiva cada. Infelizmente, ambos s\303\243o para as s\303\251ries com raiz indicial LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEiY0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRIjBGJ0Y5Rjk=, como vemos pelas solu\303\247\303\265esrsolve(R1, u(n));ersolve(op(remove(has,R2,x)), u(n));Obtendo a equa\303\247\303\243o recursiva para a raiz indicial LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEiY0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JJm1mcmFjR0YkNigtSSNtbkdGJDYkUSIxRidGOS1GUzYkUSIyRidGOS8lLmxpbmV0aGlja25lc3NHRlUvJStkZW5vbWFsaWduR1EnY2VudGVyRicvJSludW1hbGlnbkdGZ24vJSliZXZlbGxlZEdGPS1GLDYjUSFGJ0Y5 que ser\303\241 considerada a seguir.
<Text-field style="Heading 1" layout="Heading 1"><Font encoding="UTF-8">O Algoritmo "Manual de V\303\264o" para a Recurs\303\243o</Font></Text-field>A equa\303\247\303\243o recursiva para uma equa\303\247\303\243o diferencial pode ser obtida por uma t\303\251cnica efetiva que aparece no The Maple Flight Manual (Ellis, Lodi, Johnson, Schwalbe, 1992, Brooks/Cole). Por causa das limita\303\247\303\265es do Maple em lidar com somas infinitas, substitui-se a soma infinita por uma soma finita da 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 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictSSVtc3ViR0YkNiUtRiw2JVEic0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21uR0YkNiRRIjFGJy9GOVEnbm9ybWFsRicvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJ0YrRj8= e LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictSSVtc3ViR0YkNiUtRiw2JVEic0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21uR0YkNiRRIjJGJy9GOVEnbm9ybWFsRicvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJ0YrRj8= s\303\243o inteiros positivos dependentes de problema que garantem que a soma expanda bastantes termos para adquirir todas as contribui\303\247\303\265es relevantesdos coeficientes na equa\303\247\303\243o diferencial. Na equa\303\247\303\243o diferencialde;substitu\303\255mos Y1 := Sum(a[n]*x^(n+c), n=k-2..k+2);para obterq1 := eval(de, y(x)=value(Y1));Escrevendo isso como um polin\303\264mio e extraindo todos os termos em 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 leva aq2 := select(has, simplify(q1), x^(k+c-1));do qual obtemos a recurs\303\243ofactor(isolate(q2, a[k]));de acordo comRecursionEqn;obtido anteriormente.
<Text-field style="Heading 1" layout="Heading 1"><Font encoding="UTF-8">S\303\251ries Truncadas</Font></Text-field>Em uma variedade de maneiras, o Maple pode fornecer a solu\303\247\303\243o de uma equa\303\247\303\243o diferencial como uma s\303\251rie truncada. Primeiramente, temosdsolve(de, y(x), series);Nessa forma, uma expans\303\243o truncada da solu\303\247\303\243o geral, n\303\243o \303\251 claro que que o termo sem o fator LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictSSZtc3FydEdGJDYjLUYsNiVRInhGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRidGKy9GOVEnbm9ybWFsRic= \303\251 atualmente um polin\303\264mio. Alternativamente, temosDEtools[formal_sol](de, y(x));com a solu\303\247\303\243o geral substitu\303\255da por aproxima\303\247\303\265es aos membros do conjunto fundamental.Dado cada recurs\303\243oQ0;
Q1;o comando rectoproc escreve um processo cujos valores s\303\243o membros da sequ\303\252ncia satisfazendo a recurs\303\243o. Desse modo, temos os procedimentosC0 := gfun[rectoproc](Q0, u(k)):
C1 := gfun[rectoproc](Q1, u(k)):que geram os respectivos membrosseq(C0(k), k=0..6);
seq(C1(k), k=0..6);Note que em cada caso, LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRidGKy1JJW1zdWJHRiQ2JS1GLDYlUSNfQ0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21uR0YkNiRRIjBGJy9GOVEnbm9ybWFsRicvJS9zdWJzY3JpcHRzaGlmdEdGPkYrRj8= \303\251 usado como valor inicial na sequ\303\252ncia.N o caso de um comando tal comodsolve(de, y(x), formal_series);n\303\243o produz duas s\303\251ries sobre LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRIjBGJ0Y5Rjk= de modo queSlode[hypergeom_formal_sol](de, y(x));produz, o Research Fellow Dr. Edgardo Cheb-Terab do Maple sugere usardsolve(de, y(x), series);para determinar que existe uma solu\303\247\303\243o da forma LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2I1EhRictSSZtc3FydEdGJDYjLUYsNiVRInhGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRidGKy1GIzYmLUYsNiVRImdGJ0Y1RjgtSSNtb0dGJDYtUTAmQXBwbHlGdW5jdGlvbjtGJy9GOVEnbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRkgvJSlzdHJldGNoeUdGSC8lKnN5bW1ldHJpY0dGSC8lKGxhcmdlb3BHRkgvJS5tb3ZhYmxlbGltaXRzR0ZILyUnYWNjZW50R0ZILyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGVy1JKG1mZW5jZWRHRiQ2JC1GIzYkRjJGREZERkRGK0ZE. Para encontrar LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Ji1GLDYlUSJnRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEwJkFwcGx5RnVuY3Rpb247RicvRjhRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZCLyUpc3RyZXRjaHlHRkIvJSpzeW1tZXRyaWNHRkIvJShsYXJnZW9wR0ZCLyUubW92YWJsZWxpbWl0c0dGQi8lJ2FjY2VudEdGQi8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRlEtSShtZmVuY2VkR0YkNiQtRiM2JC1GLDYlUSJ4RidGNEY3Rj5GPkY+RitGPg==, fa\303\247a a mudan\303\247a de vari\303\241veis 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 viaTemp := PDEtools[dchange](y(x)=sqrt(x)*g(x), de, [g(x)]);e extraiaDE := remove(has,simplify(Temp),sqrt(x));do qual chegamos \303\240 conclus\303\243oQg := gfun[diffeqtorec](DE, g(x), v(k));e essa solu\303\247\303\243orsolve(Qg, v(k));que compara favoravelmente comU1;a recurs\303\243o encontrada anteriormente para a raiz indicial 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