BLUES iteration applied to nonlinear ordinary differential equations for wave propagation and heat transfer
arXiv:2012.11303 · doi:10.1088/1751-8121/abcf57
Abstract
The iteration sequence based on the BLUES (Beyond Linear Use of Equation Superposition) function method for calculating analytic approximants to solutions of nonlinear ordinary differential equations with sources is elaborated upon. Diverse problems in physics are studied and approximate analytic solutions are found. We first treat a damped driven nonlinear oscillator and show that the method can correctly reproduce oscillatory behaviour. Next, a fractional differential equation describing heat transfer in a semi-infinite rod with Stefan-Boltzmann cooling is handled. In this case, a detailed comparison is made with the Adomian decomposition method, the outcome of which is favourable for the BLUES method. As a final problem, the Fisher equation from population biology is dealt with. For all cases, it is shown that the solutions converge exponentially fast to the numerically exact solution, either globally or, for the Fisher problem, locally.
arXiv comment24 pages, 13 figures
References in corpus (7)
- An appetizer to modern developments on the Kardar-Parisi-Zhang universality class
- Creation and manipulation of stable dark solitons and vortices in microcavity polariton condensates
- Soliton Interaction with External Forcing within the Korteweg-de Vries Equation
- Bacterial range expansions on a growing front: Roughness, Fixation, and Directed Percolation
- BLUES function method in computational physics
- Analytic iteration procedure for solitons and traveling wavefronts with sources
- Fluxon interaction with the finite-size dipole impurity
Cited by in corpus (3)
- The BLUES function method applied to partial differential equations and analytic approximants for interface growth under shear
- Epidemic processes with vaccination and immunity loss studied with the BLUES function method
- The BLUES function method for second-order partial differential equations: application to a nonlinear telegrapher equation