Lidstone-Euler Second-Type Boundary Value Problems: Theoretical and Computational Tools

General nonlinear high odd-order differential equations with Lidstone-Euler boundary conditions of second type are treated both theoretically and computationally. First, the associated interpolation problem is considered. Then, a theorem of existence and uniqueness of the solution to the Lidstone-Euler second-type boundary value problem is given. Finally, for a numerical solution, two different approaches are illustrated and some numerical examples are included to demonstrate the validity and applicability of the proposed algorithms.

Automated summary

This study investigates the theoretical and computational treatment of general high odd-order nonlinear differential equations with Lidstone-Euler second-type boundary conditions. The associated interpolation problem is considered, followed by a theorem on the existence and uniqueness of solutions to the boundary value problem. Two different numerical solution approaches are illustrated, with numerical examples demonstrating the validity and applicability of the algorithms proposed.