Solu\303\247\303\265es num\303\251ricas de equa\303\247\303\265es diferenciais Exemplo 1) Resolver uma equa\303\247\303\243o diferencial numericamente Calcula-se a solu\303\247\303\243o num\303\251rica de y' = f(x,y) com a condi\303\247\303\243o inicial acrescentando-se a op\303\247\303\243o type=numeric ( o defaut \303\251 type = exact) no comando dsolve NomeLista := dsolve( { D(y)(x) = f(x,y), y(a)=b }, y(x), type=numeric) O retorno \303\251 o "procedimento" ( proc... end ) usado para calcular uma lista que cont\303\251m os pares de pontos [ [x=x0, y(x)=y(x0 )] , [x=x1,y(x)=y(x1)], .....,[x=xN,y(x)=y(xN)] ] Esta lista n\303\243o aparece explicitamente. Podemos explicitar o elemento da lista dado por [ , ] digitando-se NomeLista(xK); Por exemplo, a equa\303\247\303\243o diferencial y' = y com a condi\303\247\303\243o inicial , tem como solu\303\247\303\243o

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Exemplo 2) Plotar uma solu\303\247\303\243o num\303\251rica Os dados num\303\251ricos obtidos com o type = numeric pode ser plotado com o comando odeplot dentro da biblioteca plots. Para isto devemos explicitar o intervalo do dom\303\255nio da vari\303\241vel independente x. Podemos usar ainda todas as demais op\303\247\303\265es de plot[options] odeplot(NomeLista, [VarEixoX, VarEixoY], Dom\303\255nio, Op\303\247\303\265esDEplot[options], ) Afim de compar a precis\303\243o na plotagem , no exemplo abaixo plotamos a Lista1 obtida acima no intervalo [-2,2] de dois modos: primeiramente com 5 pontos e depois com 25 pontos, No segundo desenho invertemos a posi\303\247\303\243o dos eixos

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Exemplo 3) Outros m\303\251todos num\303\251ricos O Maple pode empregar v\303\241rios m\303\251todos de integra\303\247\303\243o num\303\251rica tais como : method = rkf45, method = dverk78, method = classical, method = gear, method = mgear, method = lsode, or method = taylorserie. O default \303\251 o method = rkf45 ( Fehlberg fourth-fifth order Runge-Kutta method). Para maiores informa\303\247\303\265es consulte dsolve[numeric] , dsolve[rkf45] , dsolve[dverk78] , dsolve[classical] , dsolve[gear] , dsolve[mgear] , dsolve[lsode] , dsolve[taylorseries] , `,` unexpected No exemplo a seguir vamos calcular a solu\303\247\303\243o num\303\251rica de y'=y com , atrav\303\251s do m\303\251todo "classic" e dispondo os resultados num formato especial com a op\303\247\303\243o value=array

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value = array([-1.7,1.0,1.5]));

Solu\303\247\303\265es por s\303\251ries de pot\303\252ncias de equa\303\247\303\265es diferenciais Calcula-se as solu\303\247\303\265es num\303\251ricas de equa\303\247\303\265es diferenciais y' = f(x,y) colocando-se type=series como op\303\247\303\243o do comando dsolve. O Maple pode dar a solu\303\247\303\243o geral do desevolvimento da s\303\251rie de pot\303\252ncias em x = 0 (default) com

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ou desenvolver a s\303\251rie num ponto x = a se damos o valor inicial

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A ordem da s\303\251rie Order = n (o default \303\251 n = 6 ) deve ser escolhida antes de se calcular a solu\303\247\303\243o. Como nas solu\303\247\303\265es exatas de equa\303\247\303\265es diferencias, o retorno \303\251 uma "igualdade" na qual o segundo membro \303\251 uma s\303\251rie. Se queremos usar a aproxima\303\247\303\243o apresentada pelo Maple como uma express\303\243o alg\303\251brica , devemos converter a s\303\251rie num polin\303\264mio e depois us\303\241-lo. Por exemplo, a equa\303\247\303\243o n\303\243o tem solu\303\247\303\243o exata no Maple V

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solu\303\247\303\243o no ponto x = 1

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JSFH