广义非线性Sine-Gordon方程的一个隐式差分格式及其Richardson外推
An Implicit Finite Difference Scheme for Generalized Nonlinear Sine-Gordon Equation and Richardson Extrapolation
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摘要: 对广义非线性Sine-Gordon方程的初边值问题提出了一个修正的隐式差分格式, 该新格式在不降低其理论精度的情况下, 减少了计算量。另外还对新格式进行了Richardson外推, 进一步提高了计算的精度。数值实验表明本文的格式和方法是有效的。Abstract: A modified implicit finite difference method for the initial-boundary value problem of Generalized nonlinear Sine-Gordon equation is presented in this paper.This scheme reduces the calculation and still is O(τ2+h2).In addition, applying Richardson extrapolation the order of approximation can reach O(τ2+h4).Numerical experiments demonstrate that the method is effective.
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