CAS Application to the Construction of High-Order Difference Schemes for Solving Poisson Equation

摘要

In the present work, a computer algebra system (CAS) is applied for constructing a new difference scheme of high-accuracy order for solving boundary-value problem for Poisson equation. The formulae of the difference scheme are constructed in the symbol form in CAS. CAS are used for translation of complex formulae to C++ language operators, calculation of arithmetic values of the constructed scheme coefficients and matrix elements of a system of linear algebraic equations for the discrete problem approximating the initial difference problem. Efficiency of the CAS application and of the schemes constructed with its help is shown.