Parabolic partial differential equations (PDEs) are fundamental in modelling a wide range of diffusion processes in physics, finance and engineering. The numerical ...

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 ...

Fourier analysis and numerical methods have long played a pivotal role in the solution of differential equations across science and engineering. By decomposing complex functions into sums of ...

A mathematician has developed new methods for the numerical solution of ordinary differential equations. These so-called multirate methods are highly efficient for large systems, where some components ...

Abstract: Analytically solving complex or large-scale differential equations is often difficult or even impossible, making numerical integration methods indispensable. However, as all numerical ...

Abstract: Partial differential equations (PDEs) provide an accurate representation of mathematical and physical relationships in many modern engineering applications. In this paper, we utilize the ...

An entirely new framework is established for developing various single- and multi-step formulations for the numerical integration of ordinary differential equations. Besides polynomials, ...

The Bi-Section method finds roots of non-linear equations using interval bisection. Initial Range Calculation: Determines an initial maximum range ((-|xmax|, |xmax ...