A Composition Method For Solving Burgers-type Equations

The Runge-Kutta method, as a kind of classical numerical methods, is widely used in solving a variety of differential equations. In this work, we composite the Runge-Kutta method according to certain rules and get two new higher preci-sion composition methods. Furthermore, numerical experiments are presented to demonstrate the efficiency and feasibility of the composition method.First, we construct a composite method based on the explicit Runge-Kutta method. The new composition method is used to solve KdV-Burgers equation, an ODE about time variable t whose space variable is discretized by Chebyshev collocation method. Numerical experiments depict that the composition method has higher accuracy than the Sinc method. Besides, this method is used to solve (1+1) and (2+1) dimensional coupled Burgers equations. Numerical experiments show that the composited method has higher precision of at least one orders’ magnitude than the Runge-Kutta method that are not composited.Then, a composite method based on the self-adjoint Runge-Kutta method is constructed. We use this method to solve the (1+1)-dimensional Burgers equation. Numerical experiments show that this composited method has high computational stability and more accurate than the Runge-Kutta method that are not composited under certain conditions.The last, the (1+1) dimensional coupled Burgers equations’s space variable is discretized by partitioned. Numerical experiment depict that the method can reduce the absolute error.