A Legendre-Petrov-Galerkin and Chebyshev collocation method for third-order differential equations
A Legendre-Petrov-Galerkin and Chebyshev collocation method for third-order differential equations
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DOI：
10.1137/s0036142999361505
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发表时间：
2000-12-14
影响因子：
2.9
通讯作者：
Sun, WW
中科院分区：
文献类型：
--
作者：
Ma, HP;Sun, WW
提出了一种求解三阶微分方程的勒让德-彼得罗夫-伽辽金(LPG)方法。通过选择合适的基函数，可以有效地实现该方法。此外，这种新的方法使我们能够得到L-2范数下的最优收敛速度。将该方法应用于一些非线性问题，如对非线性项采用切比雪夫配置法处理的KdV方程。它是Legendre Petrov Galerkin和Chebyshev配置法(LPG-CC)。给出了数值实验，验证了理论结果。
A Legendre Petrov Galerkin ( LPG) method for the third-order differential equation is developed. By choosing appropriate base functions, the method can be implemented efficiently. Also, this new approach enables us to derive an optimal rate of convergence in L-2-norm. The method is applied to some nonlinear problems such as the Korteweg de Vries ( KdV) equation with the Chebyshev collocation treatment for the nonlinear term. It is a Legendre Petrov Galerkin and Chebyshev collocation ( LPG-CC) method. Numerical experiments are given to con rm the theoretical result.