Solutions of partial differential equations by restrictive pade approximation method

This thesis is consists of four sections.In the first section, Pade Approximations for time-dependent partial differential equation and Restrictive Pade Approximation in which errors are totally removed at certain points by the help of this approximation will be given. The Pade series relates the value of a differentiable function at any point to its first and higher order derivatives at a reference point, and consequently the first or higher order derivatives at the reference point can be obtained in terms of the sampled values of the functions. In the solution to approximate the exponential matrix function by using Restrictive Pade Approximation will be showed.In the second section, with the help of Restrictive Pade Approximations will be done nümerical solution of the heat conduction equation. For this solution, stability analysis will be done, and truncation error will be found. Effectiveness of Restrictive Pade Approximation will be compared with other methods by considered problems. Heat conduction equation with the help of Maple programming language with the help of Restrictive Pade Approximation the solution are discussed.In the third section, to find Fisher and Burger-Fisher equations nümerical solution, Restrictive Pade Approximation method will be applied. The results obtained are compared with other methods.In the fourth section, nümerical solution of convection-diffusion equation will be made with the help of Restrictive Pade Approximation. Effectiveness of Restrictive Pade Approximation will be compared with other methods by considered problems.Keywords : Pade approximation, Restrictive Pade approximation, Heat Conduction equation, Burger-Fisher equation, Convection-Diffusion equation.