Help with fsolve command, in solving system of equations acquired by spectral collocation.

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Tanya Sharma 2021-1-28

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https://ww2.mathworks.cn/matlabcentral/answers/729203-help-with-fsolve-command-in-solving-system-of-equations-acquired-by-spectral-collocation

评论： Ehab Elsayed 2021-11-18

采纳的回答： Walter Roberson

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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.

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Priya M 2021-10-6

@Tanya Sharma

Hi...Im priya...also doing Spectral collocation technique in my research...i have some doubts...can you please help me how to give an input in MATLAB.

my mail id :priya.jeni28@gmail.com

Ehab Elsayed 2021-11-18

@Tanya Sharma Hi... Im Ehab, i run your program Tanya and solve the set of algebraic equations in MATLAB? using "solve (F)" we get the solution for N=3 only but no solution for N>3 why???? My email ehab_math@yahoo.com

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采纳的回答

Walter Roberson 2021-1-28

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https://ww2.mathworks.cn/matlabcentral/answers/729203-help-with-fsolve-command-in-solving-system-of-equations-acquired-by-spectral-collocation#answer_608133

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().