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

Algorithm 4

Implementation of BCM for solving (25)–(27).

Step : Collocating the initial condition (26):

for

for

;

;

;

;

end

end

Step : Collocating the boundary conditions (27):

variable discretization:

for

for

;

;

;

;

end

variable discretization:

for

for

;

;

;

;

end

Step : Collocating the main equation (25):

for

for

for

;

;

end

end

end

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

;

;

maxit = ;

tol = ;

= gmres(, , tol, maxit)