Author/Authors :
Ezzati، R نويسنده Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran. , , Shakibi، K نويسنده .Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran , , Ghasemimanesh، M نويسنده Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran. ,
Abstract :
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 $L_{D}$, 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.
