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Finite difference spectral collocation schemes for the solutions of boundary value problems.
A O Adewumi1, A A Aderogba1, S O Akindeinde2
1Department of Mathematics, Obafemi Awolowo University, 220005, Ile-Ife, Nigeria.
Heliyon
|January 3, 2024
Summary
Novel numerical methods using finite difference techniques accurately solve one-dimensional Bratu
Area of Science:
- Numerical analysis
- Computational mathematics
- Applied mathematics
Background:
- Bratu's problem is a class of nonlinear boundary value problems.
- Existing numerical methods may face challenges with accuracy and convergence for these problems.
Purpose of the Study:
- To introduce novel numerical approaches for solving one-dimensional Bratu's problems.
- To adapt these methods for boundary value problems with Robin conditions.
Main Methods:
- Application of standard and nonstandard finite difference methods.
- Utilization of the quasilinearization technique to convert nonlinear problems into linear ones.
- Employing Chebyshev polynomials and Sumudu transform for function approximation and trial function generation.
Main Results:
- The proposed finite difference schemes provide accurate approximations for Bratu's problems.
- The modified scheme effectively solves boundary value problems with Robin conditions.
- Numerical outcomes demonstrate the efficacy and convergence of the developed methods.
Conclusions:
- The novel numerical schemes are efficient and accurate for solving one-dimensional Bratu's problems.
- The quasilinearization technique combined with Chebyshev polynomials and Sumudu transform offers a robust approach.
- The methods show promise for addressing related boundary value problems.
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