Troesch’s problem: A numerical study with cubic trigonometric B-spline method

Abstract

This research paper presents a numerical investigation of Troesch’s problem using the collocation method based on the cubic trigonometric B-Spline technique. Troesch’s problem is a well-known BVP that arises in the field of mathematical physics and engineering. The objective of this study is to provide an accurate and efficient numerical solution to Troesch’s problem. Our method utilizes the properties of cubic trigonometric B-splines with collocation technique to approximate the solution of Troesch’s problem. The method is employed to satisfy the boundary conditions, resulting in a system of algebraic equations. A comprehensive error analysis is conducted to assess the accuracy and convergence of the proposed scheme. The obtained numerical results are compared with the exact solution, where available, and with other existing numerical methods to validate the accuracy and efficiency of the proposed technique. The significance and relevance of this work lie in its ability to provide highly accurate solutions to Troesch’s problem. Furthermore, the proposed method exhibits good convergence properties and demonstrates superiority over other numerical techniques in terms of accuracy and efficiency. These findings have practical implications in the field of mathematical physics and engineering, where precise solutions to Troesch’s problem can greatly enhance the understanding and optimization of various systems.

Keywords

• Troesch’s problems
• Trigonometric B-spline
• Boundary value problem
• Error analysis
• Collocation method