A meshfree radial basis function method for nonlinear phi-four equation

Document Type : Research Paper


Department of Mathematics, Lovely Professional University, Phagwara, Punjab, India


Radial basis function pseudospectral method is applied to obtain the solution for nonlinear Phi-four time dependant equation with nonhomogeneous initial and boundary conditions.  In this method, the efficient pseudospectral technique is combined with radial basis function to get the best of it. In the proposed method, the radial basis kernels are used to discretize the space derivatives in the Phi-four equation where as a time stepping technique is used to accord with the temporal part of the solution. The given Phi-four equation is transformed into a set of ordinary equations. An ode solver is used to solve the ordinary equations. An effective approach is used to choose the value of the shape parameter for radial basis function. Numerical results are presented to check the validity and accuracy of the method to solve the Phi-four equation.