Approximate Solutions of Nonlinear Partial Differential Equations Using B-Polynomial Bases

A multivariable technique has been incorporated for guesstimating solutions of Nonlinear Partial Differential Equations (NPDE) using bases set B-Polynomials (B-polys). To approximate the anticipated solution NPD equation, a linear product variable coefficients ai(t) and Bi(x) B-polys employed. Additionally, quantities in are determined Galerkin method minimizing errors. Before minimization process is to take place, NPDE converted into an operational matrix equation which, when inverted, yields values undefined expected solution. The nonlinear terms combined initial guess iterated until converged obtained. valid established appropriate degree B-poly basis employed, conditions imposed on before inverse invoked. However, accuracy depends number certain expressed multidimensional variables. Four examples have worked out show efficacy two-dimensional technique. estimated compared with known exact excellent agreement found between them. In calculating equations, currently employed provides higher-order precision finite difference method. present could be readily extended solving complex partial differential equations problems.