An initial value theory for linear causal boundary value problems

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

INITIAL-BOUNDARY VALUE PROBLEMS FOR LINEAR PDEs: THE ANALYTICITY APPROACH

It is well-known that the main difficulties associated with the study of initial-boundary value problems for linear PDEs is given by the presence of unknown boundary values in any method of solution. To deal efficiently with this difficulty, we have recently proposed two alternative (but interrelated) methods in Fourier space: the Analitycity approach and the Elimination by Restriction approach...

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...

INITIAL-BOUNDARY VALUE PROBLEMS FOR LINEAR AND SOLITON PDEs

Evolution PDEs for dispersive waves are considered in both linear and nonlinear integrable cases, and initial-boundary value problems associated with them are formulated in spectral space. A method of solution is presented, which is based on the elimination of the unknown boundary values by proper restrictions of the functional space and of the spectral variable complex domain. Illustrative exa...

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.