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A novel hybrid scheme for solving stiff nonlinear partial differential equations. (English) Zbl 1175.65122

A new mixed numerical technique based on spectral method, exponential time differencing, contour integral and Taylor expansion (SETDCT) is proposed to solve nonlinear time dependent high-order stiff PDEs. Applications to the numerical solution of both stiff dispersive and dissipative equations are presented. It is proved that the order of truncation error for the proposed scheme is \(O((\Delta t)^4)\). Numerical results are given to demonstrate efficiency of the scheme.

MSC:

65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
65D30 Numerical integration
35Q53 KdV equations (Korteweg-de Vries equations)
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