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A Nonlinear Integration Scheme for Evolutionary Differential Equations

H.-L. XU, Z.-L. WANG


In this paper, we investigate the construction of numerical schemes for evolutionary differential equations on their long-term behavior at large time steps. We consider Weierstrass’ theory instead of Taylor’s approach. It is found that for polynomials of finite terms, the exact difference results are always reachable for any sizes of time steps. It shows that the nonlinear integration scheme is capable of constructing accurate difference methods, and also has the superiority of time step size insensitivity


evolutionary differential equation, initial-value problem, numerical approximation, large-time-step computingText

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