Ishak Hashim
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View article: Derivative-Free Method for Nonlinear Systems with Some Real-Life Applications
Derivative-Free Method for Nonlinear Systems with Some Real-Life Applications Open
This study implements a very effective derivative-free approach for root determination in the context of nonlinear equations. The use of Homeier’s third-order technique, which is based on the application of Newton’s theorem with regard to …
View article: Finite Difference Scheme for One-dimensional Coupled Parabolic System with Blow-up
Finite Difference Scheme for One-dimensional Coupled Parabolic System with Blow-up Open
This study aims to find an efficient technique to estimate the blow-up time (BUT) of one-dimensional semilinear coupled parabolic systems. Firstly, a fully discrete finite difference formula is derived with a nonfixed time-stepping formula…
View article: An Iterative Fractional Operational Matrix Method for Solving Fractional Undamped Duffing Equation with High Nonlinearity
An Iterative Fractional Operational Matrix Method for Solving Fractional Undamped Duffing Equation with High Nonlinearity Open
This study presents a novel iterative fractional operational matrix method for solving the highly nonlinear fractional undamped Duffing equation. The proposed method efficiently approximates the solution by transforming the original fracti…
View article: Thermal performance and heat dissipation analysis of hybrid nanofluids in microchannel heat sinks using Yamada-Ota and Hamilton-Crosser models
Thermal performance and heat dissipation analysis of hybrid nanofluids in microchannel heat sinks using Yamada-Ota and Hamilton-Crosser models Open
This manuscript investigates the dynamics of a hybrid nanofluid based on the Yamada-Ota and Hamilton-Crosser models, comprising copper, titanium oxide, and aluminium oxide with a blood base fluid. The hybrid nanofluid, applied to sensor su…
View article: A New Higher-Order Scheme for Multiple Roots with Unknown Multiplicity
A New Higher-Order Scheme for Multiple Roots with Unknown Multiplicity Open
In this work, we propose a new efficient iterative method to find multiple roots of nonlinear equations with unknown multiplicity n. The new scheme is free from the second derivative and consists of three steps derived from Enhanced Halley…
View article: Numerical investigation of heat and mass transfer for unsteady multiphase flow in a vented cavity filled with hybrid nanofluid
Numerical investigation of heat and mass transfer for unsteady multiphase flow in a vented cavity filled with hybrid nanofluid Open
Effective heat and mass transfer is crucial for enhancing efficiency and performance, particularly under varying flow conditions in devices such as heat exchangers, microfluidic systems, and chemical reactors. The current study investigate…
View article: A general definition of the fractal derivative: Theory and applications
A general definition of the fractal derivative: Theory and applications Open
In this paper, we introduce a general definition of the fractal derivative with respect to a function $ \psi $, in the context of the order $ 0 < \alpha\leq 1 $ and the function $ \psi(\Theta) $. This novel definition generalizes the class…
View article: Exact and numerical solutions of the generalized breaking soliton system: Insights into non-linear wave dynamics
Exact and numerical solutions of the generalized breaking soliton system: Insights into non-linear wave dynamics Open
In this paper, we examined the (2+1)-dimensional generalized breaking soliton system (GBSS), an adaptable framework that accurately describes the three-dimensional, wave-dominated interactions occurring in many non-linear media, i.e., flui…
View article: Exact and numerical approaches for solitary and periodic waves in a (2+1)-dimensional breaking soliton system with adaptive moving mesh
Exact and numerical approaches for solitary and periodic waves in a (2+1)-dimensional breaking soliton system with adaptive moving mesh Open
In this study, we examined a (2+1)-dimensional generalized breaking soliton system (GBSS) using both analytical and numerical methods. By applying a generalized direct algebraic method, we derived exact solutions that displayed a variety o…
View article: Traveling wave reductions and adaptive moving mesh computations for the improved Boussinesq equation
Traveling wave reductions and adaptive moving mesh computations for the improved Boussinesq equation Open
This paper is concerned with the analytical and numerical study of the improved Boussinesq (IB) equation, a nonlinear dispersive model for applications in fluid dynamics, elasticity, geophysics, and nonlinear optics. Two systematic symboli…
View article: Proficient trigonometrical-fitted two-derivative multistep collocation methods in predictor-corrector approach: Application to perturbed Kepler problem
Proficient trigonometrical-fitted two-derivative multistep collocation methods in predictor-corrector approach: Application to perturbed Kepler problem Open
An efficient trigonometrical-fitted two-derivative multistep collocation (TF-TDMC) method using Legendre polynomials up to order five as the basis functions, has been developed for solving second-order ordinary differential equations with …
View article: Enhancement of cooling process of hot blocks mounted inside a horizontal channel using flexible baffles — Alternative arrangement
Enhancement of cooling process of hot blocks mounted inside a horizontal channel using flexible baffles — Alternative arrangement Open
In this paper, two heated blocks and three flexible baffles that are alternately placed on the upper and bottom sides of a rectangular channel are used to replicate the transient heat and air movement. The novelty of this research is the u…
View article: A Numerical Method for Investigating Fractionali Volterra-Fredholm Integro-Differential Model
A Numerical Method for Investigating Fractionali Volterra-Fredholm Integro-Differential Model Open
In this article, we investigate the fractional Volterra-Fredholm integro-differential equations. These equations appear in several applications such as control theory, biology, and particle dynamics in physics. We derive a numerical method…
View article: Numerical Finite-Difference Approximations of a Coupled Reaction-Diffusion System with Gradient Terms
Numerical Finite-Difference Approximations of a Coupled Reaction-Diffusion System with Gradient Terms Open
This study focuses on the derivation of explicit and implicit finite difference formulas.The objective of this study is to derive an estimation of the blow-up time for a coupled reaction-diffusion system incorporating gradient terms, emplo…
View article: Implementing Bernstein Operational Matrices to Solve a Fractional‐Order Smoking Epidemic Model
Implementing Bernstein Operational Matrices to Solve a Fractional‐Order Smoking Epidemic Model Open
This paper leverages the Bernstein operational matrices method for the first time in order to resolve the nonlinear fractional smoking epidemic model presented in terms of Caputo’s fractional derivative. An approximate solution is derived …
View article: A cotangent fractional Gronwall inequality with applications
A cotangent fractional Gronwall inequality with applications Open
This article presents the cotangent fractional Gronwall inequality, a novel understanding of the Gronwall inequality within the context of the cotangent fractional derivative. We furnish an explanation of the cotangent fractional derivativ…
View article: B-spline method for solving fractional delay differential equations
B-spline method for solving fractional delay differential equations Open
In this paper, we used the fractional collocation method based on the B-spline basis to derive the numerical solutions for a special form of fractional delay differential equations (DFDEs). The fractional derivative used is defined in the …
View article: https://www.isr-publications.com/jmcs/articles-12886-numerical-finite-difference-approximations-of-a-coupled-parabolic-system-with-blow-up
https://www.isr-publications.com/jmcs/articles-12886-numerical-finite-difference-approximations-of-a-coupled-parabolic-system-with-blow-up Open
This paper is concerned with the numerical blow-up time for a coupled system of two one-dimensional semilinear parabolic equations with zero Dirichlet boundary conditions.Firstly, we derive the semi-discrete problem and prove that the blow…
View article: Oscillatory Behavior of Higher-Order Differential Equations with Delay Terms
Oscillatory Behavior of Higher-Order Differential Equations with Delay Terms Open
The aim of this research is to study the oscillatory properties of higher -order delay half linear differential equations with non-canonical operators. Two methods for establishing some new conditions for the oscillation of all solutions o…
View article: Evaluation of Speed, Flow, and Density Performance under Different Severity of Speed Bumps
Evaluation of Speed, Flow, and Density Performance under Different Severity of Speed Bumps Open
Speed bumps are effective traffic calming tools that give transportation experts the ability to regulate vehicle speeds and enhance safety in particular areas. Despite being often utilized in populated areas, they are more common on other,…
View article: An Improved Symmetric Numerical Approach for Systems of Second-Order Two-Point BVPs
An Improved Symmetric Numerical Approach for Systems of Second-Order Two-Point BVPs Open
This study deals with the numerical solution of a class of linear systems of second-order boundary value problems (BVPs) using a new symmetric cubic B-spline method (NCBM). This is a typical cubic B-spline collocation method powered by new…
View article: Spectral technique with convergence analysis for solving one and two-dimensional mixed Volterra-Fredholm integral equation
Spectral technique with convergence analysis for solving one and two-dimensional mixed Volterra-Fredholm integral equation Open
A numerical approach based on shifted Jacobi-Gauss collocation method for solving mixed Volterra-Fredholm integral equations is introduced. The novel technique with shifted Jacobi-Gauss nodes is applied to reduce the mixed Volterra-Fredhol…
View article: The Novel Mittag-Leffler–Galerkin Method: Application to a Riccati Differential Equation of Fractional Order
The Novel Mittag-Leffler–Galerkin Method: Application to a Riccati Differential Equation of Fractional Order Open
We present a new numerical approach to solving the fractional differential Riccati equations numerically. The approach—called the Mittag-Leffler–Galerkin method—comprises the finite Mittag-Leffler function and the Galerkin method. The erro…