Enclosures and semi-analytic discretization of boundary value problems

Direct discretization methods for optimization boundary value problems in DAE

Practical optimal control problems, e.g., from the areas of robotics or chemical engineering are typically nonlinear and of high dimension. For these problem classes, direct discretization methods have proved to be very eecient and reliable tools. They allow the simultaneous solution of the optimization and the simulation task, therefore reducing the amount of computational eeort considerably. ...

Analytic matrix technique for boundary value problems in applied plasticity

An efficient matrix formalism for finding power series solutions to boundary value problems typical for technological plasticity is developed. Hyperbolic system of two first order quasilinear PDEs that models two-dimensional plastic flow of von Mises material is converted to the telegraph equation by the hodograph transformation. Solutions to the boundary value problems are found in terms of hy...

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.

Existence of multiple solutions for Sturm-Liouville boundary value problems

In this paper, based on variational methods and critical point theory, we guarantee the existence of infinitely many classical solutions for a two-point boundary value problem with fourth-order Sturm-Liouville equation; Some recent results are improved and by presenting one example, we ensure the applicability of our results.

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