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Question: Collecting coefficients in differential expression

Question:Collecting coefficients in differential expression

mskalsi 290 Maple
diff collect
February 17 2016
0

Dear all

I have problem related to collection of coefficient of differtials in differential expression containing multiple dependent variables and we want to collect coefficient wrt to selected dependent variables. Please see attached Maple file for details.

 


> 

with(PDEtools):
> 

DepVars := [u(x, t), v(x, t), a[1](t), a[2](t), a[3](t), b[1](t), b[2](t), b[3](t), r(x, t), s[1](x, t), p[1](x, t), s[2](x, t), p[2](x, t)]

[u(x, t), v(x, t), a[1](t), a[2](t), a[3](t), b[1](t), b[2](t), b[3](t), r(x, t), s[1](x, t), p[1](x, t), s[2](x, t), p[2](x, t)]

 (1)
> 

alias(u = u(x, t), v = v(x, t), a[1] = a[1](t), a[2] = a[2](t), a[3] = a[3](t), b[1] = b[1](t), b[2] = b[2](t), b[3] = b[3](t), r = r(x, t), s[1] = s[1](x, t), p[1] = p[1](x, t), s[2] = s[2](x, t), p[2] = p[2](x, t))

u, v, a[1], a[2], a[3], b[1], b[2], b[3], r, s[1], p[1], s[2], p[2]

 (2)

Suppose we differential expression like:

> 

a[1]*(diff(u, x))*s[1]*u-2*a[1]*u*(diff(r, x))*(diff(u, x))+2*a[2]*(diff(v, x))*s[2]*v-2*a[2]*v*(diff(r, x))*(diff(v, x))-(diff(a[3], t))*r*(diff(u, x))/a[3]+diff(p[1], t)+a[3]*(diff(p[1], x, x, x))+(diff(r, t))*(diff(u, x))+(diff(s[1], t))*u-(diff(a[3], t))*s[1]*u/a[3]-s[1]*a[2]*v*(diff(v, x))-(diff(a[3], t))*a[1]*u*(diff(u, x))/a[3]-(diff(a[3], t))*a[2]*v*(diff(v, x))/a[3]-3*(diff(r, x))*p[1]+(diff(a[1], t))*u*(diff(u, x))+(diff(a[2], t))*v*(diff(v, x))+a[2]*(diff(v, x))*p[2]+a[2]*v^2*(diff(s[2], x))+a[2]*v*(diff(p[2], x))+a[1]*u*(diff(p[1], x))+a[1]*(diff(u, x))*p[1]+a[1]*u^2*(diff(s[1], x))+3*a[3]*(diff(s[1], x))*(diff(u, x, x))+3*a[3]*(diff(s[1], x, x))*(diff(u, x))+a[3]*(diff(r, x, x, x))*(diff(u, x))-(diff(a[3], t))*p[1]/a[3]-3*r*(diff(r, x))*(diff(u, x))-3*(diff(r, x))*s[1]*u+a[3]*(diff(s[1], x, x, x))*u+3*a[3]*(diff(r, x, x))*(diff(u, x, x)) = 0

3*a[3]*(diff(diff(r, x), x))*(diff(diff(u, x), x))+3*a[3]*(diff(s[1], x))*(diff(diff(u, x), x))+3*a[3]*(diff(diff(s[1], x), x))*(diff(u, x))+a[3]*(diff(diff(diff(r, x), x), x))*(diff(u, x))+a[3]*(diff(diff(diff(s[1], x), x), x))*u+diff(p[1], t)+(diff(r, t))*(diff(u, x))+(diff(s[1], t))*u-3*(diff(r, x))*p[1]+a[3]*(diff(diff(diff(p[1], x), x), x))-(diff(a[3], t))*a[1]*u*(diff(u, x))/a[3]-(diff(a[3], t))*a[2]*v*(diff(v, x))/a[3]+a[1]*(diff(u, x))*s[1]*u-2*a[1]*u*(diff(r, x))*(diff(u, x))+2*a[2]*(diff(v, x))*s[2]*v-2*a[2]*v*(diff(r, x))*(diff(v, x))-(diff(a[3], t))*r*(diff(u, x))/a[3]-(diff(a[3], t))*s[1]*u/a[3]-s[1]*a[2]*v*(diff(v, x))+(diff(a[1], t))*u*(diff(u, x))+a[1]*u*(diff(p[1], x))+a[2]*v*(diff(p[2], x))+a[2]*v^2*(diff(s[2], x))+a[2]*(diff(v, x))*p[2]+a[1]*(diff(u, x))*p[1]+a[1]*u^2*(diff(s[1], x))-(diff(a[3], t))*p[1]/a[3]-3*r*(diff(r, x))*(diff(u, x))-3*(diff(r, x))*s[1]*u+(diff(a[2], t))*v*(diff(v, x)) = 0

 (3)

We can collect coefficients of differential like u[x], u[x, x], v[x], u, vin following manner:

The Procedure
   

 

 

Now how can we collect coefficents with respect to u[x], u[x, x], v[x], u, vso that differential expression (3) appear as
"(......)*u+(.......)*v+(......)*u[x]+(........)*uu[x]+(.........)vv[x]+(........)u[xx] =0....................."????????""

> 

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Download Collecting_Coefficients_in_Differential_Expression.mw

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