On One Class of Multipoint Boundary-Value Problems for a Second-Order Linear Functional-Differential Equation

Abdullaev, A. R.; Skachkova, E. A.

doi:10.1007/s10958-018-3761-9

Cited by 3 publications

(1 citation statement)

References 4 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Analytical solutions of a class of boundary value problems, involving the governing differential equation or slight generalizations of the one considered in (1), but with different and/or simpler differential operators, have been proposed in [7][8][9][10]. Existence theorems for nonlocal multipoint boundary value problem and IDEs via analytical methods are given in [11][12][13]. Boundary value problems B: XX of the type of (1) for the specific case of ln Articles ТЕОРЕТИЧЕСКАЯ И ПРИКЛАДНАЯ МАТЕМАТИКА have been studied by Vassiliev, Parasidis, Providas in [14,15], using the extension method.…”

Section: Introductionmentioning

confidence: 99%

An exact solution method for Fredholm integro-differential equations

Tsilika

2019

ICS

View full text Add to dashboard Cite

Introduction: Linear boundary value problems for Fredholm ordinary integro-differential equations are seldom consideredwith integral boundary conditions in the literature. In our case, integro-differential equations are subject to multipoint or nonlocalintegral boundary conditions. It should be noted that finding exact solutions even for multipoint problems or problems with nonlocalintegral boundary conditions with a differential equation is a difficult task. Purpose: Finding the uniqueness and existencecriterion of solutions for Fredholm ordinary integro-differential equations with multipoint or nonlocal integral boundary conditionsand obtaining exact solutions in closed form of such problems. Results: Within the class of abstract operator equations, for thespecial case of Fredholm integro-differential equations with multipoint or nonlocal integral boundary conditions, a criterion for theexistence and uniqueness of an exact solution is proved and the analytical representation of the solution is given. A direct methodanalytically solving such problems is proposed, in which all calculations are reproducible in any program of symbolic calculations.If the user sets the input parameters and the initial conditions of the problem, the computer codes check the conditions of existenceand uniqueness and of solution generate the analytical solution. The stages of the solution method are illustrated by twoexamples. The article uses computer algebra system Mathematica to demonstrate the results.

show abstract

Section: Introductionmentioning

confidence: 99%

An exact solution method for Fredholm integro-differential equations

Tsilika

2019

ICS

View full text Add to dashboard Cite

show abstract

Exact Solution to Systems of Linear First-Order Integro-Differential Equations with Multipoint and Integral Conditions

Baiburin

Providas

2019

Springer Optimization and Its Applications

View full text Add to dashboard Cite

Exact solution method for Fredholm integro-differential equations with multipoint and integral boundary conditions. Part 1. Extention method

Vassiliev¹,

Parasidis

Providas

2018

Informacionno-upravlâûŝie sistemy

View full text Add to dashboard Cite

Introduction:Boundary value problems for differential and integro-differential equations with multipoint and non-local boundary conditions often arise in mechanics, physics, biology, biotechnology, chemical engineering, medical science, finances and other fields. Finding an exact solution of a boundary value problem with Fredholm integro-differential equations is a challenging problem. In most cases, solutions are obtained by numerical methods.Purpose:Search for necessary and sufficient solvability conditions for abstract operator equations and their exact solutions. Results: A direct method is proposed for the exact solution of a certain class of ordinary differential or Fredholm integro-differential equations with separable kernels and multlpolnt/lntegral boundary conditions. We study abstract equations of the formBu = Au -gF(Au) = fandB1u = A2u -qF(Au) -gF(A2u) = fwith non-local boundary conditionsΦ(u ) =NѰ(u )andΦ(u ) =NѰ(u ),Φ(Au) =DF(Au) +NѰ(Au), respectively, where A is a differential operator,qandgare vectors,DandNare matrices, andF,ΦandѰare functional vectors. This method is simple to use and can be easily incorporated into any Computer Algebra System (CAS). The upcoming Part 2 of this paper will be devoted to decomposition method for this problem where the operatorB1is quadratic factorable.

show abstract

On One Class of Multipoint Boundary-Value Problems for a Second-Order Linear Functional-Differential Equation

Cited by 3 publications

References 4 publications

An exact solution method for Fredholm integro-differential equations

An exact solution method for Fredholm integro-differential equations

Exact Solution to Systems of Linear First-Order Integro-Differential Equations with Multipoint and Integral Conditions

Exact solution method for Fredholm integro-differential equations with multipoint and integral boundary conditions. Part 1. Extention method

Contact Info

Product

Resources

About