Euler Method: The simplest numerical method for solving ODEs, which uses the derivative to project forward. [ y_{n+1} = y_n + h \cdot f(x_n, y_n) ] Heun's Method (Improved Euler Method): A two-step ...

In Numerical Methods Lib, fully automate the process of running the program through files: add the ability to add the main directory for the configuration file (the process architecture will still be ...

Exponential integrators represent an innovative class of numerical methods designed to address the challenges posed by stiff differential equations. By incorporating the matrix exponential to treat ...

Abstract: Differential equations are frequently used to analyze and design analog circuits and numerically solved from computation of difference equations. The equivalent difference equations are ...

Abstract: The pendulum problem is one of the most studied topics in the field of Physics. In fact, in most cases, the simplest case is analyzed, so that in the less complex techniques given to ...

摘要: In this paper, a new iterative formula for solving ordinary and partial nonlinear differential equations is derived based on the combination between Bernstein’s polynomial and the Adomian ...

ABSTRACT: Nonlinear differential equations are often extremely difficult to solve. Even three hundred years after its formulation, an analytical solution to the nonlinear Riccati differential equation ...