Abstract: In this paper, by using the theories and methods of mathematical analysis and computer algebra, a reliable algorithm of finite difference method for solving singular perturbation problems was established, a new matlab procedure ehssp was implemented, too. Several linear and non-linear problems are presented to illustrate the implementation of the program. [Copyright &y& Elsevier]
Abstract: In this paper, by using theories of stochastic process and computer algebra, a reliable algorithm for computing the high-order transition probability matrix of finite Markov chain is established, a new mechanical procedure markovproc is established, too. The procedure markovproc give not only the exact expression of the Markov chains, but also the limiting probability. Some examples are presented to illustrate the implementation of the algorithm. [Copyright &y& Elsevier]
Abstract: In this paper, by using the theories and methods of mathematics analysis and computer algebra, a reliable algorithm for solving high-order nonlinear Volterra–Fredholm integro-differential equations was established, and a new Maple procedure voltfredproc was established too. The results of the examples indicated that the procedure voltfredproc of Taylor polynomial method is simple and effective, and could provide an accuracy approximate solution or exact solution of the high-order nonlinear Volterra–Fredholm integro-differential equation. This would be useful for solving integro-differential equation, integral equations and ordinary differential equation. [Copyright &y& Elsevier]