# Differential Equations and Numerical Methods

**Type:** Topics  
**Canonical URL:** https://scholariq.org/topics/differential-equations-and-numerical-methods/

## Facts

| Field | Value |
| --- | --- |
| Citations | 598,554 |
| Description | This cluster of papers focuses on numerical methods and analysis for solving singularly perturbed problems, particularly in the context of convection-diffusion and reaction-diffusion equations. The research covers topics such as boundary layers, finite difference schemes, asymptotic analysis, parameter-robust methods, and adaptive meshes to accurately solve these challenging problems. |
| Domain | Physical Sciences |
| Field | Mathematics |
| OpenAlex ID | https://openalex.org/T12727 |
| Works | 59,617 |

## Topic papers all

- [<i>N</i>th-Order Operator Splitting Schemes and Nonreversible Systems](https://scholariq.org/papers/i-n-i-th-order-operator-splitting-schemes-and-nonreversible-systems/)
- [Homotopy perturbation method to time-fractional diffusion equation with a moving boundary condition](https://scholariq.org/papers/homotopy-perturbation-method-to-time-fractional-diffusion-equation-with-a-moving/)
- [On fourth-order elliptic boundary value problems](https://scholariq.org/papers/on-fourth-order-elliptic-boundary-value-problems/)
- [Approximate solution of the Bagley–Torvik equation by hybridizable discontinuous Galerkin methods](https://scholariq.org/papers/approximate-solution-of-the-bagley-torvik-equation-by-hybridizable-discontinuous/)
- [On the asymptotic solutions of singulary perturbed differential systems of fractional order](https://scholariq.org/papers/on-the-asymptotic-solutions-of-singulary-perturbed-differential-systems-of/)
- [An Investigation on the Approximate Controllability of Non-instantaneous Impulsive Hilfer Sobolev-Type Fractional Stochastic System Driven by the Rosenblatt Process and Poisson Jumps](https://scholariq.org/papers/an-investigation-on-the-approximate-controllability-of-non-instantaneous/)
- [A numerical algorithm based on extended cubic B-spline functions for solving time-fractional convection-diffusion-reaction equation with variable coefficients](https://scholariq.org/papers/a-numerical-algorithm-based-on-extended-cubic-b-spline-functions-for-solving/)
- [Applications of mechanical engineering mathematics : Solving Neumann problem with discontinuous coefficients](https://scholariq.org/papers/applications-of-mechanical-engineering-mathematics-solving-neumann-problem-with/)

## Topic researchers

Showing 12 of 20.

- [Tasawar Hayat](https://scholariq.org/researchers/tasawar-hayat/)
- [George Em Karniadakis](https://scholariq.org/researchers/george-em-karniadakis/)
- [Thomas J.R. Hughes](https://scholariq.org/researchers/thomas-j-r-hughes/)
- [A. J. Simmons](https://scholariq.org/researchers/a-j-simmons/)
- [Richard Bellman](https://scholariq.org/researchers/richard-bellman/)
- [J. L. Wright](https://scholariq.org/researchers/j-l-wright/)
- [Ji‐Huan He](https://scholariq.org/researchers/ji-huan-he/)
- [George H. Weiss](https://scholariq.org/researchers/george-h-weiss/)
- [Tosio Kato](https://scholariq.org/researchers/tosio-kato/)
- [Philip Holmes](https://scholariq.org/researchers/philip-holmes/)
- [Brian J. Hoskins](https://scholariq.org/researchers/brian-j-hoskins/)
- [YangQuan Chen](https://scholariq.org/researchers/yangquan-chen/)

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Source: ScholarIQ — public research metadata, principally OpenAlex. See https://scholariq.org/sources/ for provenance and https://scholariq.org/methodology/ for what these figures mean.