Numerical solution of the general rosenau equation by meshless kernel based method of lines

Most of the partial differential equations are emerged from different areas of science and engineering are non-linear equations. Several numerical methods are used to solve these equations. Commonly used numerical techniques are finite differences, finite elements and finite volume methods. These methods are depend on a mesh. These mesh dependent methods posses some limitations such as mesh generation, spatial dependence, slow convergence rate, instability and low accuracy. Another class of numerical methods are meshfree methods. Meshfree methods are expected to give superior numerical results than mesh based methods. Meshfree methods using radial basis functions have higher convergence rate. These methods provide accurate numerical solution by using large space step sizes. In this thesis, numerical solution of General Rosenau-RLW equation which is a nonlinear time dependent partial differential equation is evaluated by meshless kernel based method of lines using radial basis functions. When the present method is applied to the equation a system of ordinary differential equations is obtained. Therefore this obtained system of ordinary differential equations is solved by using Adams-Bashforth-Moulton method which is a multi-step method. The method is applied to some test problems and results are compared with other numerical techniques in literature. Performance of the method is studied by L2 and L∞ error norms and conservation of mass and energy. Stability of the method is shown by Von Neumann stability analysis. The numerical results show that using present method is effective and provides very accurate solutions. Therefore it is seen that the meshless kernel based method of lines can be applied to these types of non-linear partial differential equations. Keywords: Method of lines, Rosenau-RLW equation, Radial Basis Functions