Using Multiquadric Quasi-Interpolation For Solving Kawahara Equation

Multiquadric quasi-interpolation is a useful instrument in approximation theory and its applications. in this paper, a numerical approach for solving kawahara equation (ke) is developed by using multiquadric quasi-interpolation method. obtaining numerical solution of ke by multiquadric quasi-interpolation is done by a recurrence relation. in this recurrence relation, the approximation of derivative is evaluated directly without the need to solve any linear system of equation. also, by combining hermite interpolation and quasi-interpolation ld,another way to solve ke is obtained. the ke occurs in the theory of magneto-acoustic waves in a plasma and in the theory of shallow water waves with surface tension. we test the method in two examples and compare the numerical and exact results.