Ordinary differential equations (ODEs) are also called initial value problems because a time zero value for each first-order differential equation is needed. The following is an example of a ...

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 ...

ABSTRACT: In this paper, a class of operator-differential equation of the first order with multiple characteristics is considered, for which the initial boundary value problem on the semi-axis is well ...

Abstract: Methods of functional approximation for the computer solution of initial value partial differential equation problems provide a device by which these solutions can be approximated by those ...

Abstract: In this paper, we consider the existence and uniqueness of positive solutions to fractional integro-differential equations by using mixed monotone operator. On this basis, we investigate the ...

In this paper, a numerical approach is developed for solving initial value problem of linear fractional Volterra integro-differential equations. The approximate solution is substituted into the model ...

Boundary value problems (BVPs) and spectral analysis constitute fundamental areas in the study of differential equations. These topics not only underpin theoretical advances in mathematical analysis ...

Fuzzy differential equations (FDEs) extend classical differential equations by incorporating uncertainty through fuzzy numbers. This mathematical framework is particularly valuable for modelling ...

In this paper, the boundary value problems for second order singularly perturbed delay differential equations are treated. A generic numerical approach based on finite difference is presented to solve ...

This project provides Fourier neural operators (FNOs) for solving partial differential equations (PDEs) and an ordinary differential equation (ODE) integrator, all written in JAX/Flax.