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mostafajani

Dr. Mostafa Jani

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9 years, 3 days
Shahid Beheshti University
Postdoctoral researcher

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Ph.D., Applied Mathematics, Research interests: Numerical analysis, Numerical methods for partial differential equations, Fractional PDEs, Spectral methods, Machine learning, Computational mechanics

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These are answers submitted by mostafajani

The first equation has two unknowns F[0]...

mostafajani 35
June 04 2017
0 1

The first equation has two unknowns F[0] and F[1]. If you know F[0] then you can solve all the remaining equations like the following:

 

restart; SS := sum(F[k-m]*(sum(F[m-L]*(sum(F[L-j]*F[j], j = 0 .. L)), L = 0 .. m)), m = 0 .. k); F[0] := 1; n := 8; for k from 0 to n do eq[k] := -(F[k]+.5*(sum((k-m+1)*F[k-m+1]*F[m], m = 0 .. k))+0.5e-1*SS)/(k+1); assign(solve({eq[k]}, {F[k+1]})) end do; seq(F[k], k = 0 .. n)

I assumed F[0]:=1: It gives the other F[k] for k from 0 to n.

Otherwise, i.e., if all F[k] are unknown you can solve the linear system

restart; SS := sum(F[k-m]*(sum(F[m-L]*(sum(F[L-j]*F[j], j = 0 .. L)), L = 0 .. m)), m = 0 .. k); n := 8; for k from 0 to n do eq[k] := -(F[k]+.5*(sum((k-m+1)*F[k-m+1]*F[m], m = 0 .. k))+0.5e-1*SS)/(k+1); assign(solve({seq(eq[k], k = 0 .. n)}, {seq(F[k], k = 0 .. n)})) end do; seq(F[k], k = 0 .. n);

which gives zero for all F[k].

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