Initial-value methods for discrete boundary value problems

Solving Discrete Initial- and Boundary-Value Problems

Multivariate linear recurrences appear in such diverse elds of mathematics as combinatorics, probability theory, and numerical resolution of partial diierential equations. Whereas in the univariate case the solution of a constant-coeecient recurrence always has a rational generating function, this is no longer true in the multivariate case where this generating function can be non-rational, non...

Approximating Initial-Value Problems with Two-Point Boundary-Value Problems: BBM-Equation

Discrete Boundary-value Problems

We consider multivariate sequences, deened by a partial linear recurrence equation together with appropriate boundary conditions. The domain of deenition of these sequences is the rst orthant of the integer lattice, restricted in some dimensions to an initial segment of the nonnegative integers. By means of the kernel method we obtain an explicit expression for the generating function of the so...

L2-transforms for boundary value problems

In this article, we will show the complex inversion formula for the inversion of the L2-transform and also some applications of the L2, and Post Widder transforms for solving singular integral equation with trigonometric kernel. Finally, we obtained analytic solution for a partial differential equation with non-constant coefficients.

Reproducing Kernel Methods for Solving Linear Initial-boundary-value Problems

In this paper, a reproducing kernel with polynomial form is used for finding analytical and approximate solutions of a second-order hyperbolic equation with linear initial-boundary conditions. The analytical solution is represented as a series in the reproducing kernel space, and the approximate solution is obtained as an n-term summation. Error estimates are proved to converge to zero in the s...