In this tutorial, I demonstrate how to solve boundary value differential equations using the Finite Difference Method in Python. Learn step-by-step how to implement this numerical technique, ...

In this tutorial, I walk you through solving boundary value problems using the Shooting Method in Python. Learn how to apply this numerical technique to find solutions for differential equations with ...

Backward stochastic differential equations (BSDEs) have emerged as a pivotal mathematical tool in the analysis of complex systems across finance, physics and engineering. Their formulation, generally ...

We propose a new approach to constructing weak numerical methods for finding solutions to stochastic systems with small noise. For these methods we prove an error ...

An important characterization of a numerical method for first order ODE's is the region of absolute stability. If all eigenvalues of the linear problem y' = Ay are inside this region, the numerical ...

Abstract: Iterative solver of linear systems is a key component for numerical solutions of differential equations, playing an important role in numerical analysis and scientific computing. While there ...

Maxwell's equations form the cornerstone of electromagnetic theory, offering a complete description of how electric and magnetic fields interact with matter. In combination with state‐of‐the‐art ...