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Hi,

I am solving a coupled system of equations using spectral collocation scheme,

u''+a1*t=a2;

t''=0;

with b.c

u=0,t=0.5 at y=0;

u=0,t=1 at y=1;

The set of equations at (N+1) collocation points will be described as:

D2*U+a1*T=a2;

D2*T=0;

with

U_0 = 0, T_0=1

U_N = 0, T_N=0.5

where

D2 is the differentiation matrix of order(N+1), given by D2=D*D

U and T are the vectors of unknowns

a1=30;

a2=-12;

with given boundary conditions, how can solve the set of algebraic equations in MATLAB?

Can it be solved using "fsolve"?

As I do now know how to express the vectores U and T in the code.

Walter Roberson
on 28 Jan 2021

You are mixing notations it looks like to me. D*U would be used more for working with Laplace transforms. In the space you are working in, which is not the laplace space, you do not use multiplication notation and you cannot treat D like a variable to be solved for, and cannot use fsolve.

I would suggest that you use the symbolic toolbox and dsolve().

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