Efficient method for solving highly oscillatory ordinary differential equations with applications to physical systems
F. J. Agocs, W. J. Handley, A. N. Lasenby, M. P. Hobson
Abstract
This paper presents a novel numerical method for efficiently solving ordinary differential equations with rapidly oscillating solutions. The method steps along the numerical solution, dynamically switching between using a Runge---Kutta estimate and the Wentzel---Kramers---Brillouin approximation in areas of slowly varying frequency, thus being able to skip over many periods of oscillation in one step, whilst maintaining accuracy even at high frequencies.
Topics & Concepts
Ordinary differential equationMathematicsOscillation (cell signaling)Applied mathematicsNumerical analysisMathematical analysisPhysical systemDifferential equationNumerical stabilityCollocation methodControl theory (sociology)Stability (learning theory)L-stabilityDelay differential equationExplicit and implicit methodsNumerical partial differential equationsDifferential algebraic equationPartial differential equationExact differential equationIntegrating factorFloquet theoryBackward differentiation formulaComputer scienceDifferential (mechanical device)Quantum Mechanics and Non-Hermitian PhysicsNumerical methods for differential equationsPulsars and Gravitational Waves Research