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

Algorithm 1

Implementation of BCM for solving (1)–(3).

Step : Collocating the main equation (1):

for

for

;

;

end

end

Step : Collocating the boundary conditions (3):

for

;

;

;

;

end

Step : Collocating the initial condition (2):

for

;

end

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

;

;

maxit = ;

tol = ;

= gmres (, , tol, maxit)