3 papers
math.DS2026
On the independence of the slow and fast scales in multiple-scale expansions, with application to Van der Pol's equation
Gregory Kozyreff, John R. King
When implementing the method of multiple scales, one is traditionally instructed to treat the slow and fast time scales as if they were independent. Despite the intuitive motivatio…
math.AP2023
Complex-plane singularity dynamics for blow up in a nonlinear heat equation: analysis and computation
M. Fasondini, J. R. King, J. A. C. Weideman
Blow-up solutions to a heat equation with spatial periodicity and a quadratic nonlinearity are studied through asymptotic analyses and a variety of numerical methods. The focus is…
math.CA2019
Termination points and homoclinic glueing for a class of inhomogeneous nonlinear ordinary differential equations
Jack S. Keeler, Mark G. Blyth, John R. King
Solutions to the class of inhomogeneous nonlinear ordinary differential equations taking the form \[u'' + u^2 = αf(x) \] for parameter are studied. The problem is define…