Hardware acceleration is crucial in enhancing performance, efficiency, and scalability across a wide range of computing applications. In this work, we have implemented a hardware accelerator ...

Abstract: In the present paper, we analyse the geometric properties of projected Runge–Kutta methods for the solution of index 3 differential–algebraic equations in the Hessenberg form. We show that ...

The purpose of this study is the design of efficient methods for the solution of an ordinary differential system of equations arising from the semidiscretization of a hyperbolic partial differential ...

Mathematics of Computation, Vol. 59, No. 200 (Oct., 1992), pp. 403-420 (18 pages) We apply Runge-Kutta methods to linear partial differential equations of the form u t (x, t) = L (x, ∂)u(x, t) + f(x, ...

This paper mainly presents Euler method and fourth-order Runge Kutta Method (RK4) for solving initial value problems (IVP) for ordinary differential equations (ODE). The two proposed methods are quite ...

The Bi-Section method finds roots of non-linear equations using interval bisection. Initial Range Calculation: Determines an initial maximum range ((-|xmax|, |xmax|)) for root existence. Calculation ...

Abstract: Considering a linear system of delay integro-differential equations with a constant delay whose zero solution is asympototically stable, this paper discusses the stability of numerical ...

ABSTRACT: In this paper, we use the classic mathematical model SIR with the three differential equations as a non-linear system and combine it with the Runge-Kutta numerical method of the fourth order ...

Finite element methods provide a robust, mature family of discretizations for partial differential equations, as they provide rigorous theory, general geometry, and fast solvers. Modern trends in ...