Physical Sciences and Mathematics Commons^™

Approximate Solutions Of Nonlinear Partial Differential Equations Using B-Polynomial Bases, Muhammad I. Bhatti, Md. Habibur Rahman, N. Dimakis

Physics and Astronomy Faculty Publications and Presentations

A multivariable technique has been incorporated for guesstimating solutions of Nonlinear Partial Differential Equations (NPDE) using bases set of B-Polynomials (B-polys). To approximate the anticipated solution of the NPD equation, a linear product of variable coefficients ai(t) and Bi(x) B-polys has been employed. Additionally, the variable quantities in the anticipated solution are determined using the Galerkin method for minimizing errors. Before the minimization process is to take place, the NPDE is converted into an operational matrix equation which, when inverted, yields values of the undefined coefficients in the expected solution. The nonlinear terms of the NPDE are combined in the …