Solving the third-kind Volterra integral equation via the boundary value technique: Lagrange polynomial versus fractional interpolation

2022 ◽  
Vol 414 ◽  
pp. 126685
Author(s):  
Hao Chen ◽  
Junjie Ma
Keyword(s):  
Integral Equation ◽  
Volterra Integral Equation ◽  
Boundary Value ◽  
Lagrange Polynomial ◽  
The Third ◽  
Polynomial Versus

scholarly journals To the solution of the Solonnikov-Fasano problem with boundary moving on arbitrary law x = γ(t).

2021 ◽  
Vol 101 (1) ◽  
pp. 37-49
Author(s):  
M.T. Jenaliyev ◽  
◽  
M.I. Ramazanov ◽  
A.O. Tanin ◽  
◽  
...  
Keyword(s):  
Integral Equation ◽  
Integral Operator ◽  
Boundary Value Problem ◽  
Heat Equation ◽  
Volterra Integral Equation ◽  
Boundary Value ◽  
Nonzero Solution ◽  
Initial Moment ◽  
Homogeneous Integral Equation

In this paper we study the solvability of the boundary value problem for the heat equation in a domain that degenerates into a point at the initial moment of time. In this case, the boundary changing with time moves according to an arbitrary law x = γ(t). Using the generalized heat potentials, the problem under study is reduced to a pseudo-Volterra integral equation such that the norm of the integral operator is equal to one and it is shown that the corresponding homogeneous integral equation has a nonzero solution.

scholarly journals Application Local Polynomial and Non-polynomial Splines of the Third Order of Approximation for the Construction of the Numerical Solution of the Volterra Integral Equation of the Second Kind

2021 ◽  
Vol 20 ◽  
Author(s):  
I. G. Burova
Keyword(s):  
Integral Equation ◽  
Numerical Solution ◽  
Volterra Integral Equation ◽  
Numerical Experiments ◽  
Polynomial Interpolation ◽  
Order Of Approximation ◽  
Polynomial Splines ◽  
Third Order ◽  
The Third ◽  
Local Polynomial

The present paper is devoted to the application of local polynomial and non-polynomial interpolation splines of the third order of approximation for the numerical solution of the Volterra integral equation of the second kind. Computational schemes based on the use of the splines include the ability to calculate the integrals over the kernel multiplied by the basis function which are present in the computational methods. The application of polynomial and nonpolynomial splines to the solution of nonlinear Volterra integral equations is also discussed. The results of the numerical experiments are presented.

Boundary-Value Problems for Third-Order Lipschitz Ordinary Differential Equations

2014 ◽  
Vol 58 (1) ◽  
pp. 183-197 ◽  
Author(s):  
John R. Graef ◽  
Johnny Henderson ◽  
Rodrica Luca ◽  
Yu Tian
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Boundary Value Problems ◽  
Order Differential Equation ◽  
Boundary Value ◽  
Point Boundary ◽  
Third Order ◽  
Optimal Length ◽  
The Third

AbstractFor the third-order differential equationy′″ = ƒ(t, y, y′, y″), where, questions involving ‘uniqueness implies uniqueness’, ‘uniqueness implies existence’ and ‘optimal length subintervals of (a, b) on which solutions are unique’ are studied for a class of two-point boundary-value problems.

Direct integration of the third-order two point and multipoint Robin type boundary value problems

2021 ◽  
Vol 182 ◽  
pp. 411-427
Author(s):  
Nadirah Mohd Nasir ◽  
Zanariah Abdul Majid ◽  
Fudziah Ismail ◽  
Norfifah Bachok
Keyword(s):  
Boundary Value Problems ◽  
Boundary Value ◽  
Direct Integration ◽  
Third Order ◽  
The Third ◽  
Type Boundary
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