DIFFERENCE SCHEMES ARISING FROM OPERATOR SPLITTING FOR SOLVING TWO DIMENSIONAL BURGERS EQUATION

Abstract

Burgers’ equation is a fundamental partial differential equation from fluid mechanics. It occurs in various areas of applied mathematics, such as modeling of fluid dynamics and traffic flow. It relates to the Navier-Stokes equation for incompressible flow with the pressure term removed. Due to the complexity of the Analytic solution, one needs to solve the equation by using numerical methods. In this research we develope the pure Crank-Nicholson (CN) Scheme and Crank- Nicholson-Du Fort & Frankel (CN-DF) method by Operator Splitting. Crank- Nicholson-Du-Fort and Frankel is an hybrid scheme made by combining the Crank- Nicholson and Du-Fort and Frankel schemes which are both unconditionally stable but the Du-fort scheme is explicit while the Crank-Nicholson scheme is implicit. The developed schemes are solved numerically using initially solved solution via Hopf-Cole transformation and separation of variables to generate the initial and boundary conditions. Analysis of the resulting schemes was found to be unconditionally stable. The results of the hybrid scheme are found to compare well with those of the pure Crank- Nicholson.