In this session we look at basic numerical methods to help us understand the fundamentals of numerical approximations. Our objective is as follows. Implement Euler’s method as well as an improved ...

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 ...

From the perspective of numerical analysis, we employ an enhanced Euler’s method, with less approximate errors and thus more accurate, to search a better approximate optimal solution to construct a ...

This project aims to demonstrate the effectiveness of different numerical integration methods in solving dynamic differential equations. By comparing the results obtained from the Implicit Euler and ...

The Euler method is “not recommended for any practical use” [4] due to roundoff and truncation errors beyond problems with stability in numerical evaluations on computers. Despite its limitations in ...

This paper presents a class of numerical methods for the approximate solution of ordinary differential equations where the derivatives depend on the history of the solution. These methods, which are ...

Here is a plot of three things. First, the analytic solution, second the Euler method (as described above) and third the Euler method calculating position, then velocity, then acceleration.

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