Method of Lines for Quasilinear Functional Differential Equations
AbstractWe give a theorem on the estimation of error for approximate solutions to ordinary functional differential equations. The error is estimated by a solution of an initial problem for a nonlinear functional differential equation. We apply this general result to the investigation of convergence of the numerical method of lines for evolution functional differential equations. The initial boundary-value problems for quasilinear equations are transformed (by means of discretization in spatial variables) into systems of ordinary functional differential equations. Nonlinear estimates of the Perron-type with respect to functional variables for given operators are assumed. Numerical examples are given.
How to Cite
Kamont, Z., and W. Czernous. “Method of Lines for Quasilinear Functional Differential Equations”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 65, no. 10, Oct. 2013, pp. 1363–1387, https://umj.imath.kiev.ua/index.php/umj/article/view/2515.