Open Access. Powered by Scholars. Published by Universities.®
Physical Sciences and Mathematics Commons™
Open Access. Powered by Scholars. Published by Universities.®
Articles 1 - 1 of 1
Full-Text Articles in Physical Sciences and Mathematics
Oscillation-Free Method For Semilinear Diffusion Equations Under Noisy Initial Conditions, R. Corban Harwood, Likun Zhang, V. S. Manoranjan
Oscillation-Free Method For Semilinear Diffusion Equations Under Noisy Initial Conditions, R. Corban Harwood, Likun Zhang, V. S. Manoranjan
Faculty Publications - Department of Mathematics
Noise in initial conditions from measurement errors can create unwanted oscillations which propagate in numerical solutions. We present a technique of prohibiting such oscillation errors when solving initial-boundary-value problems of semilinear diffusion equations. Symmetric Strang splitting is applied to the equation for solving the linear diffusion and nonlinear remainder separately. An oscillation-free scheme is developed for overcoming any oscillatory behavior when numerically solving the linear diffusion portion. To demonstrate the ills of stable oscillations, we compare our method using a weighted implicit Euler scheme to the Crank-Nicolson method. The oscillation-free feature and stability of our method are analyzed through a …