how to remove matrix dimension error ?

Qudsiya Irum

2017 7 27

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I want solve Non Linear 1-D Heat Equation using Galerkin Finite Element Method. As I entered its ODE to solve by backward euler method, it is showing matrix dimension error. AA and MM are element stiffness and mass matrix of order(2501*2501) double respectively.

MM= spdiags([dx/6*ones(nx+1,1) 2*dx/3*ones(nx+1,1) dx/6*ones(nx+1,1)],[-1 0 1],nx+1,nx+1) 
AA = spdiags([-1/dx*ones(nx+1,1) 2/dx*ones(nx+1,1) -1/dx*ones(nx+1,1)],[-1 0 1],nx+1,nx+1); 
for mn = 2:1:M                 
T_solid_new_t(mn+1)   = {MM+ k.*AA.*dt + dt*MM.*ht}\(MM.*T_solid(mn)+(dt.*dx.*Hs)+(ht.*Tp_g.*dx.*dt))                    
end