Numerical Solutions For The Space Fractional-Order Fisher's Equation

Mohamed Adel of Benha University presents a numerical algorithm for solving the space fractional-order Fisher's equation. The method uses a compact finite difference scheme for time discretization and a Chebyshev spectral collocation method for the spatial fractional derivative. The paper includes convergence and stability analysis, supported by theorems and proofs, and provides a numerical simulation to test the algorithm's accuracy and applicability.

Use Cases

• Benchmarking numerical PDE solvers based on the described compact finite difference and spectral collocation algorithms.
• Studying convergence and stability properties of fractional derivative discretizations based on the provided theorems.
• Testing algorithm accuracy for the Fisher's equation based on the included numerical simulation.
• Developing educational material for numerical analysis of fractional-order problems based on the presented method.

Strengths

• The description details a specific numerical method combining compact finite difference and Chebyshev spectral collocation.
• The paper includes formal convergence and stability analysis with theorems and proofs.
• A numerical simulation is provided to test the algorithm's accuracy and applicability.

Limitations

• Description metadata is limited; actual data quality requires manual inspection after download.
• Column-level documentation is absent; field semantics must be inferred after download.
• Row count is unknown, which may limit suitability assessment.

Provenance

Source

Benha University

Collection Method

Theoretical and numerical treatment presented in an academic paper.