scholarly journals A fourth-order accurate difference Dirichlet problem for the approximate solution of Laplace’s equation with integral boundary condition

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Adiguzel Dosiyev ◽  
Rifat Reis
Keyword(s):  
Boundary Condition ◽  
Approximate Solution ◽  
Dirichlet Problem ◽  
Fourth Order ◽  
Integral Boundary Condition ◽  
Laplace’S Equation ◽  
Integral Boundary ◽  
Laplace's Equation

scholarly journals An Approximate Grid Solution of a Nonlocal Boundary Value Problem with Integral Boundary Condition for Laplace's Equation

2018 ◽  
Vol 22 ◽  
pp. 01016 ◽  
Author(s):  
Adıgüzel A. Dosiyev ◽  
Rifat Reis
Keyword(s):  
Boundary Condition ◽  
Boundary Value Problem ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Integral Boundary Condition ◽  
Unknown Boundary ◽  
Laplace’S Equation ◽  
Nonlocal Boundary Value Problem ◽  
Integral Boundary ◽  
Laplace's Equation

A new method for the solution of a nonlocal boundary value problem with integral boundary condition for Laplace's equation on a rectangular domain is proposed and justified. The solution of the given problem is defined as a solution of the Dirichlet problem by constructing the approximate value of the unknown boundary function on the side of the rectangle where the integral boundary condition was given. Further, the five point approximation of the Laplace operator is used on the way of finding the uniform estimation of the error of the solution which is order of 0(h2), where hi s the mesh size. Numerical experiments are given to support the theoretical analysis made.

scholarly journals A highly accurate corrected scheme in solving the Laplace's equation on a rectangle

2018 ◽  
Vol 22 ◽  
pp. 01015
Author(s):  
Adıgüzel A. Dosiyev ◽  
Hediye Sarıkaya
Keyword(s):  
Approximate Solution ◽  
Dirichlet Problem ◽  
Finite Difference Method ◽  
Grid Point ◽  
Mesh Size ◽  
Rectangular Domain ◽  
Laplace’S Equation ◽  
Laplace's Equation ◽  
Pointwise Error ◽  
Corrected Scheme

A pointwise error estimation of the form 0(ρh8),h is the mesh size, for the approximate solution of the Dirichlet problem for Laplace's equation on a rectangular domain is obtained as a result of three stage (9-point, 5-point and 5-point) finite difference method; here ρ = ρ(x,y) is the distance from the current grid point (x,y,) ε Πh to the boundary of the rectangle Π.

scholarly journals On Periodic Fractional (p, q)-Integral Boundary Value Problems for Sequential Fractional (p, q)-Integrodifference Equations

Axioms ◽  
2021 ◽  
Vol 10 (4) ◽  
pp. 264
Author(s):  
Jarunee Soontharanon ◽  
Thanin Sitthiwirattham
Keyword(s):  
Boundary Condition ◽  
Fixed Point ◽  
Boundary Value Problems ◽  
Fixed Point Theorems ◽  
Existence Results ◽  
Integral Boundary Condition ◽  
Integrodifference Equations ◽  
Integrodifference Equation ◽  
Integral Boundary ◽  
Integral Boundary Value Problems

We study the existence results of a fractional (p, q)-integrodifference equation with periodic fractional (p, q)-integral boundary condition by using Banach and Schauder’s fixed point theorems. Some properties of (p, q)-integral are also presented in this paper as a tool for our calculations.

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