Numerical Solution of Evolutionary Integral Equations with Completely Monotonic Kernel by Runge-Kutta Convolution Quadrature

被引：2

作者：

Xu, Da ^{[1
]}

机构：

[1] Hunan Normal Univ, Dept Math, Changsha 410081, Hunan, Peoples R China

来源：

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS | 2015年 / 31卷 / 01期

基金：

中国国家自然科学基金;

关键词：

evolutionary integral equation; completely monotonic kernel; time discretization; Runge-Kutta convolution quadrature; error estimates; DISCONTINUOUS GALERKIN METHOD; VOLTERRA-EQUATIONS; DIFFUSION EQUATION; INTEGRODIFFERENTIAL EQUATION; FRACTIONAL DIFFUSION; TIME DISCRETIZATION; PARABOLIC EQUATIONS; STABILITY;

D O I：

10.1002/num.21896

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the numerical solutions of the initial boundary value problems for the Volterra-type evolutionary integal equations, in which the integral operator is a convolution product of a completely monotonic kernel and a positive definite operator, such as an elliptic partial-differential operator. The equation is discretized in time by the Runge-Kutta convolution quadrature. Error estimates are derived and numerical experiments reported. (c) 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq31: 105-142, 2015

引用

页码：105 / 142

页数：38

共 50 条

[41] Numerical stability of solution to delay differential equations under resolvent condition for Runge-Kutta methods
赵景军
刘明珠
Journal of Harbin Institute of Technology, 2001, (02) : 135 - 139
[42] A class of second-order Runge-Kutta methods for numerical solution of stochastic differential equations
Abukhaled, MI
Alien, EJ
STOCHASTIC ANALYSIS AND APPLICATIONS, 1998, 16 (06) : 977 - 991
[43] Strong Runge-Kutta MethodsWith order one for Numerical Solution of Ito Stochastic Differential Equations
Soheili, Ali R.
Namjoo, Andm.
APPLIED MATHEMATICS RESEARCH EXPRESS, 2007, (01)
[44] Some embedded modified Runge-Kutta methods for the numerical solution of some specific Schrodinger equations
Simos, TE
JOURNAL OF MATHEMATICAL CHEMISTRY, 1998, 24 (1-3) : 23 - 37
[45] Convergence of Runge-Kutta-based convolution quadrature for semilinear fractional differential equations
Zhao, Jingjun
Kong, Jiameng
Xu, Yang
INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, 2024, 101 (11) : 1326 - 1340
[46] On the iterative solution of the algebraic equations in fully implicit Runge-Kutta methods
M. Calvo
S. González-Pinto
J.I. Montijano
Numerical Algorithms, 2000, 23 : 97 - 113
[47] On the iterative solution of the algebraic equations in fully implicit Runge-Kutta methods
Calvo, M
González-Pinto, S
Montijano, JI
NUMERICAL ALGORITHMS, 2000, 23 (01) : 97 - 113
[48] ERROR BOUNDS FOR THE SOLUTION TO THE ALGEBRAIC EQUATIONS IN RUNGE-KUTTA METHODS.
Dekker, K.
1600, (24):
[49] ERROR-BOUNDS FOR THE SOLUTION TO THE ALGEBRAIC EQUATIONS IN RUNGE-KUTTA METHODS
DEKKER, K
BIT, 1984, 24 (03): : 347 - 356
[50] A new code for Volterra integral equations based on natural Runge-Kutta methods
Abdi, A.
Hojjati, G.
Jackiewicz, Z.
Mahdi, H.
APPLIED NUMERICAL MATHEMATICS, 2019, 143 : 35 - 50

← 1 2 3 4 5 →