In this paper, some modifications of Adomian decomposition method are presented for solving initial value problems in ordinary differential equations. Also, the restarted and two-step methods are ...

In this work, we present some techniques applicable to Initial Value Problems when solving a System of Ordinary Differential Equations (ODE). Such techniques should be used when applying adaptive step ...

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 ...

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, 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 ...

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 ...

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 ...

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 ...

for the Rust programming language. This library provides a pure rust implementation of SciPy's solve_ivp function with slight modifications to the API to better fit Rust's design patterns. Radau: A ...

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.