Numerical Solvers for Ordinary Differential Equations
Description: This cluster of papers focuses on the development and analysis of numerical integration methods for solving differential equations, with a particular emphasis on exponential integrators, symplectic methods, time-stepping schemes, and variational integrators. The research covers a wide range of applications including the numerical solution of the Schrödinger equation, Hamiltonian systems, and matrix exponential computations.
Characteristic keywords: Runge-Kutta method, stiff ordinary differential equations, numerical solution of ODEs, numerical solution of differential equations, multistep methods, linear multistep methods, A-stability, symplectic integrators, second-order ordinary differential equations, geometric numerical integration, numerical integration of ODEs, time integration, symplectic integration, Euler method, backward differentiation formula, zero stability, order conditions, numerical integration of differential equations, implicit Runge-Kutta methods, one-step methods, explicit Runge-Kutta methods, local truncation error, exponential integrators, explicit schemes, high-order time integration
Parent subfield: Numerical Analysis
Field: Mathematics
Domain: Physical Sciences
OpenAlex ID: T11416