THE EXPONENTIAL TIME DIFFERENCING AND RATIONAL SPECTRAL COLLOCATION METHOD FOR SINGULARLY PERTURBED BURGERS-HUXLEY PROBLEM
指数时程差分与有理谱配点法求解奇异摄动Burgers-Huxley问题

The exponential time differencing (ETD) and rational spectral collocation (RSC) method are applied to numerically solve the Burgers-Huxley equation with small parameter ε, which is a nonlinear, unsteady, singularly perturbed, initial and boundary problem. The RSC method with sinh transform is employed to treat the boundary or interior layer in spatial direction while the combination of ETD and forth-order Runge-Kutta (ETDRK4) method is used to discretize the time variable. The matrix function in ETDRK4 is computed by contour integral in the complex plan, which overcomes the problem of instability. Numerical experiments illustrate the high accuracy and efficiency of our method.