New general solutions to linear Fredholm integro-differential equations and their applications on solving the boundary value problems

被引：26
作者：
Dzhumabaev, Dulat S. [1 ,2 ]
机构：
[1] MES RK, Inst Math & Math Modeling, Dept Differential Equat, 125 Pushkin Str, Alma Ata 050010, Kazakhstan
[2] Int Informat Technol Univ, Dept Math & Comp Modeling, 34A Dzhandossov Str, Alma Ata 050034, Kazakhstan
来源：
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2018年 / 327卷
关键词：
Integro-differential equation; Delta(N) general solution; Solvability criteria; Construction of solution; NUMERICAL-SOLUTIONS; COLLOCATION;
D O I：
10.1016/j.cam.2017.06.010
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
This paper introduces the Delta(N) general solution to linear Fredholm integro-differential equations and sets its properties. The conditions for existence of classical general solution and solvability criteria for the equation are provided. Necessary and sufficient conditions for solvability of linear boundary value problems are established. Algorithms for construction of the Delta(N) general solutions are obtained. This paper also proposes approximate and numerical methods to solve the boundary value problems. (C) 2017 Elsevier B.V. All rights reserved.
引用
收藏
页码：79 / 108
页数：30
相关论文
共 30 条
  • [1] [Anonymous], 1977, Functional analysis
  • [2] Boichuk A. A., 2004, GEN INVERSE OPERATOR
  • [3] A semigroup approach to an integro-differential equation modeling slow erosion
    Bressan, Alberto
    Shen, Wen
    [J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 2014, 257 (07) : 2360 - 2403
  • [4] Brunner, 2010, 7 LECTIRES THEORY NU
  • [5] Bykov Ya.V., 1957, On Some Problems in the Theory of Integro-Differential Equations
  • [6] Chafee N., 1981, Nonlinear Differential Equations, P97
  • [7] Cohen H, 2011, NUMERICAL APPROXIMATION METHODS, P1, DOI 10.1007/978-1-4419-9837-8_1
  • [8] Delves L.M., 1985, COMPUTATIONAL METHOD
  • [9] Reproducing kernel method for solving Fredholm integro-differential equations with weakly singularity
    Du, Hong
    Zhao, Guoliang
    Zhao, Chunyan
    [J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2014, 255 : 122 - 132
  • [10] On one approach to solve the linear boundary value problems for Fredholm integro-differential equations
    Dzhumabaev, D. S.
    [J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2016, 294 : 342 - 357
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