An Implicit RBF Meshless Approach For Solving Sine-Gordon And Klein - Gordon Equations

In this thesis, we propose a numerical method, which is based on radial basis function, for the solution of nonlinear sine-Gordon equation that appears extensively in classical lattice dynamics in the continuum media limit and time fractional linear Klein-Gordon equation which arises in physics respectively. In the method of nonlinear sine-Gordon equation, we make an approximation of the spatial derivatives by means of the Multiquadric quasi-interpolation,and then make an analysis of the convergence. At last, we will provide a lot of numeri-cal examples to verify the validity of the method. In the method of fractional linear Klein-Gordon equation,we first approximate the time fractional derivative of the mentioned equations by a scheme of order O(τ3-α), and then we use the Kansa approach to approximate the spatial derivatives. The results of numerical experiments are compared with analytical solutions to confirm the accuracy and efficiency of the presented scheme.