This repository contains Python scripts demonstrating various numerical methods, which are commonly taught in undergraduate Computational Physics courses. Each script includes clear explanations, ...

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I have been interested in the derivation of new and better Runge-Kutta algorithms for some time. In particular, I showed that the design of Runge-Kutta pairs by E. Fehlberg could be improved to ...

There are three interesting properties of methods for (stiff) ordinary differential equations: order, stability and efficiency of implementation. This paper constructs Runge-Kutta methods of orders 5 ...

Abstract: An explicit Runge-Kutta (RK) method with an extended stability region (ESR) can be constructed based on an RK method with a stability function corresponding to the Taylor series for the ...

Abstract: In this paper we study conditional stability properties of exponential Runge–Kutta methods when they are applied to semilinear systems of ordinary differential equations characterized by a ...