Parabolic Methods for One Dimensional Advection-Diffusion Type Equation and Application to Burger Equation

In this paper, the piecewise parabolic method is presented for solving one-dimensional advection-diffusion type equation and its application to burger equation. First, given solution domain discretized by using a uniform Discretization grid point. Next applying integration in terms of spatial variable, we converting it into system first-order ordinary differential temporarily variable. Next, Taylor series expansion obtained obtain central finite difference Then equation, solved at each specified To validate applicability proposed method, four model examples are considered specific point on domain. The stability convergent analysis present worked supported theoretical mathematical statements accuracy obtained. has been shown sense root mean square error norm L2 maximum absolute L∞ local behavior captured exactly. Numerical, exact solutions between them have graphs corresponding means tables. approximates very well quite efficient practically suited numerical result tables indicates that approximate good agreement with solution. Hence accruable solve