The Qualocation Method For Two Classes Of Evolution Equations

The qualocation method is a modification of the collocation approximations, which is similar to Petrov-Galerkin method. The method uses a cubic spline trial space and a piecewise linear test space and approximates the integrals by composite two-point Gauss quadrature rule. Compared to the collocation method and the Petrov-Galerkin method, the qualocation method improves the accuracy.In this paper, the qualocation is proposed for RLW-Burgers'equation and parabolic partial integro-differential equations. L∞(L2), L∞(H1) and L∞(H2) optimal error estimates for semidiscrete scheme for RLW-Burgers'equation are given. And then the full discrete scheme based on back Euler method along with H1 and H2 estimates is given. Then, L∞(H1) and L∞(H2) error estimates for semidiscrete scheme for parabolic partial integro-differential equation are proved, and the full discrete scheme based on back Euler method and the error estimates are obtained.