Comparison of several numerical solvers for a discretized nonlinear diffusion model with source terms
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Beny Neta
Abstract
The numerical solution of the nonlinear system of equations resulting from a real engineering problem is discussed. We use the approximate solution of a system of two nonlinear integrodifferential equations to build the nonlinear system of equations. This system can be solved by Newton’s method if the solution is differentiable, or using some derivative-free methods, such as Steffensen’s method. Here we show that Steffensen’s method does not always converge and secant method requires more iterations than Traub’s method and Newton’s method. We recommend Traub’s method in case the solution is not differentiable.
Acknowledgements
We thank Anthony P. Austin for lending a hand with the implementation of the various methods.
References
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© 2023 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- On skew derivations and antiautomorphisms in prime rings
- On the non-triviality of anisotropic Roumieu Gelfand–Shilov spaces and inclusion between them
- Solution of generalized fractional kinetic equations with generalized Mathieu series
- The generalized Drazin inverse of an operator matrix with commuting entries
- Asymptotic analysis of fundamental solutions of hypoelliptic operators
- Calculation of Reynolds equation for the generalized non-Newtonian fluids and its asymptotic behavior in a thin domain
- Double lacunary statistical convergence of Δ-measurable functions on product time scales
- On ρ-statistical convergence in neutrosophic normed spaces
- On the comparison of translation invariant convex differentiation bases
- The quasi-Zariski topology on the graded quasi-primary spectrum of a graded module over a graded commutative ring
- Some classes of topological spaces and the space of G-permutation degree
- BV capacity and perimeter in abstract Wiener spaces and applications
- New approach on the study of operator matrix
- Comparison of several numerical solvers for a discretized nonlinear diffusion model with source terms
- Localization operators and inversion formulas for the Dunkl–Weinstein–Stockwell transform
Artikel in diesem Heft
- Frontmatter
- On skew derivations and antiautomorphisms in prime rings
- On the non-triviality of anisotropic Roumieu Gelfand–Shilov spaces and inclusion between them
- Solution of generalized fractional kinetic equations with generalized Mathieu series
- The generalized Drazin inverse of an operator matrix with commuting entries
- Asymptotic analysis of fundamental solutions of hypoelliptic operators
- Calculation of Reynolds equation for the generalized non-Newtonian fluids and its asymptotic behavior in a thin domain
- Double lacunary statistical convergence of Δ-measurable functions on product time scales
- On ρ-statistical convergence in neutrosophic normed spaces
- On the comparison of translation invariant convex differentiation bases
- The quasi-Zariski topology on the graded quasi-primary spectrum of a graded module over a graded commutative ring
- Some classes of topological spaces and the space of G-permutation degree
- BV capacity and perimeter in abstract Wiener spaces and applications
- New approach on the study of operator matrix
- Comparison of several numerical solvers for a discretized nonlinear diffusion model with source terms
- Localization operators and inversion formulas for the Dunkl–Weinstein–Stockwell transform
