Bernoulli Collocation Method for Solving Linear Multidimensional Diffusion and Wave Equations with Dirichlet Boundary Conditions

Algorithm 2

Implementation of BCM for solving (4)–(6).

Step : Collocating the main equation (4):

for

for

;

;

end

end

Step : Collocating the boundary conditions (6):

for

;

;

;

;

End

Step : Collocating the initial conditions (5):

for

;

;

;

;

end

Step : Assembling the coefficient matrices and right hand side column vectors:

;

;

maxit = ;

tol = ;

= gmres(, , tol, maxit)