Results 41 to 50 of about 155 (148)

Modelling and analysis of fractal-fractional partial differential equations: Application to reaction-diffusion model

Alexandria Engineering Journal, 2020
In this paper, an extension is paid to an idea of fractal and fractional derivatives which has been applied to a number of ordinary differential equations to model a system of partial differential equations.
Kolade M. Owolabi, Abdon Atangana, Ali Akgul   +2 more
doaj   +1 more source

A Hybrid Fitted Mesh Numerical Scheme for Solving Singularly Perturbed Reaction–Diffusion Equation With Mixed Shifts

Journal of Mathematics, Volume 2026, Issue 1, 2026.
This study develops a robust hybrid numerical scheme for a class of time‐dependent, singularly perturbed differential‐difference equations characterized by a small positive parameter multiplying the highest order derivative term and mixed spatial shifts (delay and advance) in the reaction terms.
Ababi H. Ejere, Gemechis F. Duressa, Mesfin M. Woldaregay, Tekle G. Dinka, Smritijit Sen   +4 more
wiley   +1 more source

Unconditional energy dissipation and error estimate of a relaxation scheme for generalized wave equations

Demonstratio Mathematica
The law of energy dissipation is a crucial characteristic of generalized wave equations. The newly developed scalar auxiliary variable (SAV) method and its extended form, the generalized SAV (GSAV) approach, are widely used techniques for developing ...
Fu Yayun, Ma Tingting, Guo Cheng, Li Lingling   +3 more
doaj   +1 more source

Making conditionally negative definite radial basis function interpolation well-conditioned by adding cardinal basis functions

Ain Shams Engineering Journal, 2018
A class of basis functions so called well-conditioned RBF (WRBFs) has been introduced. This basis has been manipulated by adding cardinal functions to the conditionally negative definite RBFs of order 1, such as Multiquadric functions 1+(∊r)2 (MQ) and ...
Saeed Kazem, Edmund A. Chadwick, Ali Hatam   +2 more
doaj   +1 more source

Stochastic Analysis of Pine Wilt Epidemic Model With Dynamically Consistent Approximation

Complexity, Volume 2025, Issue 1, 2025.
The present study investigated the dynamics of the nonlinear stochastic pine wilt epidemic model. An extension of the stochastic to deterministic model is presented. Equilibria, positivity, boundedness, extinction, and disease persistence were studied rigorously.
Ali Raza, Mohammed Mahyoub Ali Al-Shamiri, Wafa F. Alfwzan, Muhammad Rafiq, Emad Fadhal, Nauman Ahmed, Pramita Mishra   +6 more
wiley   +1 more source

Nonstandard Finite Difference Schemes with Application to Finance: Option Pricing [PDF]

, 2010
2000 Mathematics Subject Classification: 65M06, 65M12.The paper is devoted to pricing options characterized by discontinuities in the initial conditions of the respective Black-Scholes partial differential equation. Finite difference schemes are examined
Milev, Mariyan, Tagliani, Aldo
core  

Solutions of Nonlinear Parabolic PDEs: A Novel Technique Based on Galerkin‐Finite Difference Residual Corrections

International Journal of Differential Equations, Volume 2025, Issue 1, 2025.
Numerical solutions for second‐order parabolic partial differential equations (PDEs), specifically the nonlinear heat equation, are investigated with a focus on analyzing residual corrections. Initially, the Galerkin weighted residual method is employed to rigorously formulate the heat equation and derive numerical solutions using third‐degree ...
Md. Shafiqul Islam, Nafia Mollik, Md. Kamrujjaman, Elena Kaikina   +3 more
wiley   +1 more source

A Fitted Linear Multistep Approach for Singularly Perturbed Parabolic‐Type Reaction–Diffusion Problems Using Shishkin Meshes

International Journal of Mathematics and Mathematical Sciences, Volume 2025, Issue 1, 2025.
This paper presents a class of singularly perturbed parabolic‐type reaction diffusion problems. Due to the presence of a small parameter ε, (0 < ε ≪ 1) as a diffusion coefficient, the proposed problem exhibits twin boundary layers in the neighborhood of the end points of the spatial domain near x = 0 and x = 1.
Amare Worku Demsie, Awoke Andargie Tiruneh, Endalew Getnet Tsega, Theodore Simos   +3 more
wiley   +1 more source

High-order numerical methods with stability analysis for Caputo–Riesz fractional reaction-diffusion models in three dimensions

Demonstratio Mathematica
In this paper, we propose and study a new ternary three-dimensional fractional reaction-diffusion model. The model combines Caputo fractional derivatives in time with Riesz fractional derivatives in space.
Kosari Saeed, Guan Hao
doaj   +1 more source

On the computation of roll waves [PDF]

, 2001
. The phenomenon of roll waves occurs in a uniform open-channel flow down an incline, when the Froude number is above two. The goal of this paper is to analyze the behavior of numerical approximations to a model roll wave equation ut + uux = u; u(x; 0) =
Jin, S, Jin, Shi, Shi Jin, Yong Jung Kim, Kim, Yong Jung   +4 more
core   +1 more source