Hediye Sarikaya

Near East University · Department of Mathematics

A pointwise error estimation of the form O(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)∈Πh to the boundary of...

A three stage (9-point, 5-point and 5-point) difference method for solving the Dirichlet problem for Laplace's equation on a rectangle is proposed and justified. It is proved that the proposed difference solution converges uniformly to the exact solution of order O(h⁸ |ln h|), h is the mesh size, when the boundary functions are from C9,1. Numerical...

In a rectangular domain, we discuss about an approximation of the first order derivatives for the solution of the mixed boundary value problem. The boundary values on the sides of the rectangle are supposed to have the second order derivatives satisfying the Hölder condition. Under these conditions for the approximate values of the first derivative...

We present and justify finite difference schemes with the 14-point averaging operator for the second derivatives of the solution of the Dirichlet problem for Laplace?s equations on a rectangular parallelepiped. The boundary functions ?j on the faces ?j,j = 1,2,..., 6 of the parallelepiped are supposed to have fifth derivatives belonging to the H?ld...

A 14-point difference operator is used to construct finite difference problems for the approxi- mation of the solution, and the first order derivatives of the Dirichlet problem for Laplace’s equations in a rectangular parallelepiped. The boundary functions φj on the faces Γj, j = 1, 2, …, 6 of the parallelepiped are supposed to have pth order deriv...

A pointwise error estimation of the form 0(ρh ⁸ ),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 Π h to the b...

O(h⁸) order (h is the mesh size) of accurate three-stage difference method on a square grid for the approximate solution of the Dirichlet problem for Laplace’s equation on a rectangle is proposed and justified without taking more than 9 nodes of the grid. At the first stage, by using the 9-point scheme the sum of the pure fourth derivatives of the...