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

Algorithm 3

Implementation of BCM for solving (22)–(24).

Step : Collocating the initial condition (23):

for

for

;

;

end

end

Step : Collocating the boundary conditions (24):

variable discretization:

for

for

;

;

;

;

end

variable discretization:

for

for

;

;

;

;

end

Step : Collocating the main equation (22):

for

for

for

;

;

end

end

end

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

;

;

maxit = ;

tol = ;

= gmres(, , tol, maxit)