The Alternating Segment Explicit-Implicit scheme for the dispersive equation

High-accuracy alternating segment explicit-implicit method for the fourth-order heat equation

Based on a group of new Saul’yev type asymmetric difference schemes constructed by author, a high-order, unconditionally stable and parallel alternating segment explicit-implicit method for the numerical solution of the fourth-order heat equation is derived in this paper. The truncation error is fourth-order in space, which is much more accurate than the known alternating segment explicit-impli...

The new implicit finite difference scheme for two-sided space-time fractional partial differential equation

Fractional order partial differential equations are generalizations of classical partial differential equations. Increasingly, these models are used in applications such as fluid flow, finance and others. In this paper we examine some practical numerical methods to solve a class of initial- boundary value fractional partial differential equations with variable coefficients on a finite domain. S...

Implicit-Explicit Scheme for the Allen-Cahn Equation Preserves the Maximum Principle

It is known that the Allen-Chan equations satisfy the maximum principle. Is this true for numerical schemes? To the best of our knowledge, the state-of-art stability framework is the nonlinear energy stability which has been studied extensively for the phase field type equations. In this work, we will show that a stronger stability under the infinity norm can be established for the implicit-exp...

Solving Two-Dimensional Fuzzy Partial Dierential Equation by the Alternating Direction Implicit Method

Measuring the Effectiveness of Explicit and Implicit Instruction through Explicit and Implicit Measures

Many studies have examined the effect of different approaches to teaching grammar including explicit and implicit instruction. However, research in this area is limited in a number of respects. One such limitation pertains to the issue of construct validity of the measures, i.e. the knowledge developed through implicit instruction has been measured through instruments which favor th...