Scientific Research Publishing

A Comparative Study on Numerical Solutions of Initial Value Problems (IVP) for Ordinary Differential Equations (ODE) with Euler and Runge Kutta Methods ()

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 ...
SciELO

From the Euler method to the closed-form solution of the motion of a particle influenced by linear velocity-dependent friction and arbitrary time-dependent driving force

The Euler method of numeric approximation for solving initial-value problems is applied for describing the motion of a particle influenced by linear velocity-dependent friction and arbitrary ...
Scientific Research Publishing

On the Homotopy Analysis Method and Optimal Value of the Convergence Control Parameter: Solution of Euler-Lagrange Equation ()

This paper presents, an efficient approach for solving Euler-Lagrange Equation which arises from calculus of variations. Homotopy analysis method to find an approximate solution of variational ...
Nature

Numerical Solution of Differential and Integral Equations

Numerical methods for differential and integral equations are indispensable in modern applied mathematics and engineering, offering tools to approximate complex physical phenomena where analytical ...
IEEE

Boosting Transferability of Adversarial Example via an Enhanced Euler’s Method

Abstract: Adversarial examples are intentionally designed images to force convolution neural networks to give error classification outputs. Existing attacks have ...
Wired

The Leapfrog Numerical Method

Find the forces on the object. Find the new momentum (based on the force and the small time interval) Find the new position (based on the velocity and time interval). Simple. And it even works most of ...