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- Title
Analysis of Solutions for a Sixth-Order Boundary Value Problem and Numerical Search using Nonlinear Programming Techniques.
- Authors
Machado Martinez, Andre Luís; Aparecida Pendeza Martinez, Cristiane; de Souza Pinto, Thiago; Castelani, Emerson Vitor
- Abstract
We analyzed the existence of solutions for a sixth-order boundary value problem. Initially, we established the operator that redefines the problem as a fixed-point problem and elucidated its main properties. Subsequently, we investigated the existence of solutions within the function space C*[0,1], employing the robust framework of Krasnoselskii's fixed-point theorem. Additionally, we introduced an innovative numerical methodology to explore solutions to this problem. This approach involves discretizing the problem, thereby formulating a nonlinear system. We proposed a solution strategy through the application of mathematical programming techniques for the determination of numerical solutions.
- Subjects
NUMERICAL solutions to boundary value problems; NONLINEAR programming; MATHEMATICAL programming; BOUNDARY value problems; FUNCTION spaces
- Publication
Engineering Letters, 2024, Vol 32, Issue 3, p488
- ISSN
1816-093X
- Publication type
Article