Computing Evans functions numerically via boundary-value problems

Numerically computing zeros of the Evans Function

This paper presents a method of numerically computing zeros of an analytic function for the specific application of computing eigenvalues of the Sturm-Liouville problem. The Sturm-Liouville problem is an infinite dimensional eigenvalue problem that often arises in solving partial differential equations, including the heat and wave equations. To compute eigenvalues of the Sturm-Liouville problem...

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.

Solutions of initial and boundary value problems via F-contraction mappings in metric-like space

We present sufficient conditions for the existence of solutions of second-order two-point boundary value and fractional order functional differential equation problems in a space where self distance is not necessarily zero. For this, first we introduce a Ciric type generalized F-contraction and F- Suzuki contraction in a metric-like space and give relevance to fixed point results. To illustrate...

On the Exact Multiplicity of Solutions for Boundary-value Problems via Computing the Direction of Bifurcations

We consider positive solutions of the Dirichlet problem u′′(x) + λf(u(x)) = 0 in (−1, 1), u(−1) = u(1) = 0. depending on a positive parameter λ. We use two formulas derived in [18] to compute all solutions u where a turn may occur and to compute the direction of the turn. As an application, we consider quintic a polynomial f(u) with positive and distinct roots. For such quintic polynomials we c...

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