Finite difference and homotopy analysis methods are used for the approximate solution of the initial-boundary value problem for the delay parabolic partial differential equation with the Dirichlet condition. The convergence estimates for the solution of first and second orders of difference schemes in Hölder norms are obtained. A procedure of modified Gauss elimination method is used for the solution of these difference schemes. Homotopy analysis method is applied. Comparison of finite difference and homotopy analysis methods is given on the problem.
"Approximate Solutions of Delay Parabolic Equations with the Dirichlet Condition." Abstr. Appl. Anal. 2012 (SI18) 1 - 31, 2012. https://doi.org/10.1155/2012/682752