变系数Volterra型积分微分方程的2种Legendre谱 Galerkin数值积分方法

Subjects: Mathematics >> Computational Mathematics. submitted time 2023-02-15 Cooperative journals: 《桂林电子科技大学学报》

范友康 张克磊 覃永辉

Abstract： In order to further improve the numerical accuracy of solving Volterra integro-differential, two kinds of Legendre
spectral Galerkin numerical integration methods are investigated for the Volterra-type integro-differential equation with variable
coefficients. Firstly, the Galerkin Legendre numerical integration is applied to deal with the integral term of the Volterra-
type integro-differential equations. Secondly, the Legendre tau scheme is developed for the Volterra-type integral-differential
equations with variable coefficient, and the Chebyshev-Gauss-Lobatto collocation point is used to the calculation of the
variable coefficient and integral term. Finally, by decomposing the definition interval of the function, the multi-interval Legendre
spectral Galerkin numerical integration method is also designed. Its scheme of the proposed method has symmetric
structure for odd-order model. In addition, by introducing the least squares function of the Volterra type integro-differential
equation, the Legendre spectral Galerkin least-squares numerical integration method of is constructed. The corresponding
coefficient matrix of the algebraic equation is symmetric positive. Some numerical examples are given to test the high-order
accuracy and the effectiveness of our methods.

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