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Question: Coefficients in differential expression

Question:Coefficients in differential expression

mskalsi 290 Maple
index coeff
January 19 2016
0

Dear Friends

In differential expressions(See Maple file) how to find coefficiets of dependent variable "u(x,t)" and "v(x,t)" and of their differentials ? There is command "dcoeffs(function)", but that work for single dependent variable only but in our case there are two dependent variables in consideration. There are other options like "indets", "specindex" but those do not work.

 


> 

with(PDEtools):
> 

DepVars; -1; [u(x, t), v(x, t), r[1](t), r[2](t), s[1](t), s[2](t), p[1](t), p[2](t), alpha[1](x, t), beta[1](x, t), beta[2](x, t), delta[1](x, t), delta[2](x, t)]

[u(x, t), v(x, t), r[1](t), r[2](t), s[1](t), s[2](t), p[1](t), p[2](t), alpha[1](x, t), beta[1](x, t), beta[2](x, t), delta[1](x, t), delta[2](x, t)]

 (1)
> 

alias(u = u(x, t), v = v(x, t), r[1] = r[1](t), r[2] = r[2](t), s[1] = s[1](t), s[2] = s[2](t), p[1] = p[1](t), p[2] = p[2](t), alpha[1] = alpha[1](x, t), beta[1] = beta[1](x, t), beta[2] = beta[2](x, t), delta[1] = delta[1](x, t), delta[2] = delta[2](x, t))

u, v, r[1], r[2], s[1], s[2], p[1], p[2], alpha[1], beta[1], beta[2], delta[1], delta[2]

 (2)
> 

(diff(r[1], t))*(-s[1]*u*(diff(u, x))-p[1]*((diff(u, x))*v+u*(diff(v, x)))-alpha[1]*(diff(u, x))-beta[1]*u-delta[1])/r[1]+r[1]*(diff(alpha[1]*(diff(u, x))+beta[1]*u+delta[1], x, x))+(diff(s[1], t))*u*(diff(u, x))+s[1]*(alpha[1]*(diff(u, x))+beta[1]*u+delta[1])*(diff(u, x))+s[1]*u*(diff(alpha[1]*(diff(u, x))+beta[1]*u+delta[1], x))+(diff(p[1], t))*((diff(u, x))*v+u*(diff(v, x)))+p[1]*((diff(alpha[1]*(diff(u, x))+beta[1]*u+delta[1], x))*v+(diff(u, x))*(alpha[1]*(diff(v, x))+beta[2]*v+delta[2])+(alpha[1]*(diff(u, x))+beta[1]*u+delta[1])*(diff(v, x))+u*(diff(alpha[1]*(diff(v, x))+beta[2]*v+delta[2], x)))+(diff(alpha[1], t))*(diff(u, x))+alpha[1]*(diff(alpha[1]*(diff(u, x))+beta[1]*u+delta[1], x))+(diff(beta[1], t))*u+beta[1]*(alpha[1]*(diff(u, x))+beta[1]*u+delta[1])+diff(delta[1], t)

(diff(r[1], t))*(-s[1]*u*(diff(u, x))-p[1]*((diff(u, x))*v+u*(diff(v, x)))-alpha[1]*(diff(u, x))-beta[1]*u-delta[1])/r[1]+r[1]*((diff(diff(alpha[1], x), x))*(diff(u, x))+2*(diff(alpha[1], x))*(diff(diff(u, x), x))+alpha[1]*(diff(diff(diff(u, x), x), x))+(diff(diff(beta[1], x), x))*u+2*(diff(beta[1], x))*(diff(u, x))+beta[1]*(diff(diff(u, x), x))+diff(diff(delta[1], x), x))+(diff(s[1], t))*u*(diff(u, x))+s[1]*(alpha[1]*(diff(u, x))+beta[1]*u+delta[1])*(diff(u, x))+s[1]*u*((diff(alpha[1], x))*(diff(u, x))+alpha[1]*(diff(diff(u, x), x))+(diff(beta[1], x))*u+beta[1]*(diff(u, x))+diff(delta[1], x))+(diff(p[1], t))*((diff(u, x))*v+u*(diff(v, x)))+p[1]*(((diff(alpha[1], x))*(diff(u, x))+alpha[1]*(diff(diff(u, x), x))+(diff(beta[1], x))*u+beta[1]*(diff(u, x))+diff(delta[1], x))*v+(diff(u, x))*(alpha[1]*(diff(v, x))+beta[2]*v+delta[2])+(alpha[1]*(diff(u, x))+beta[1]*u+delta[1])*(diff(v, x))+u*((diff(alpha[1], x))*(diff(v, x))+alpha[1]*(diff(diff(v, x), x))+(diff(beta[2], x))*v+beta[2]*(diff(v, x))+diff(delta[2], x)))+(diff(alpha[1], t))*(diff(u, x))+alpha[1]*((diff(alpha[1], x))*(diff(u, x))+alpha[1]*(diff(diff(u, x), x))+(diff(beta[1], x))*u+beta[1]*(diff(u, x))+diff(delta[1], x))+(diff(beta[1], t))*u+beta[1]*(alpha[1]*(diff(u, x))+beta[1]*u+delta[1])+diff(delta[1], t)

 (3)

In above differential expressions how to find coefficiets of dependent variable "u(x,t)" and "v(x,t)" and of their differentials ? There is command "dcoeffs(expr,u(x,t))", but that work for single dependent variable only but in our case there are two dependent variables in consideration. There are other options like "indets", "specindex" but those do not work.

> 

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