| Abstract: | In this study, Newton linearized finite element methods are presented forsolving semi-linear parabolic equations in two- and three-dimensions. The proposedscheme is a one-step, linearized and second-order method in temporal direction,while the usual linearized second-order schemes require at least two starting values. By using a temporal-spatial error splitting argument, the fully discrete schemeis proved to be convergent without time-step restrictions dependent on the spatialmesh size. Numerical examples are given to demonstrate the efficiency of the methods and to confirm the theoretical results. |
