Numerical Solutions of Korteweg-de Vries and Korteweg-de Vries-Burger's Equations in a Bernstein Polynomial Basis

摘要

An algorithm for approximating numerical solution to Korteweg-de Vries (KdV) and Korteweg-de Vries-Burger's (KdVB) equations in B-polynomials (Bernstein polynomial basis) is introduced. The algorithm expands the desired solution in terms of B-polynomials over a closed interval [a,b], and then makes use of the orthonormal relation of B-polynomials with its dual basis to determine the expansion coefficients to construct a solution. Matrix formulation is used throughout the entire procedure. Numerical results obtained using the current algorithm are compared with existing analytical results. Excellent agreement is found between the exact and approximate solutions.