Multimode optical fibers (MMFs) have gained renewed interest in the past decade, emerging
as a way to boost optical communication data rates in the context of an expected saturation …

This article applied the Riccati–Bernoulli (RB) sub-ODE method in order to get new exact
solutions for the long–short-wave interaction (LS) equations. Namely, we obtain …

In this paper we present fifth order Runge-Kutta method (RK5) for solving initial value
problems of fourth order ordinary differential equations. In this study RK5 method is quite …

The present study proposes a hybrid numerical technique to discuss the solution of
nonlinear reaction-diffusion equations with variable coefficients. The perturbation parameter …

In this paper, an effective numerical iterative method for solving nonlinear initial value
problems (IVPs) is presented. The proposed iterative scheme, called the Jacobi‐Picard …

Runge-Kutta method (RK5) for solving initial value problems of first order ordinary
differential equations. The two proposed methods are quite efficient and practically well …

Cubic B-Spline method for the solution of the quadratic Riccati differential equation Page 1 AIMS
Mathematics, 8(4): 9576–9584. DOI: 10.3934/math.2023483 Received: 07 October 2022 Revised …

Coupled systems of second-order ODEs are found in many areas, such as vibrations and
electric circuits. Thus, accurate and efficient solutions are of great interest. This manuscript …

The method of operational matrices is based on the Bernoulli and Shifted Legendre
polynomials which is used to solve the Falkner-Skan equation. The nonlinear differential …

In this paper, three approximate methods namely the Bernoulli, the Bernstein, and the
shifted Legendre polynomials operational matrices are presented to solve two important …