Explicit, implicit–explicit and Crank–Nicolson implicit–explicit numerical schemes for solving the generalized lubrication equation are derived. We prove that the implicit– explicit and Crank–Nicolson implicit–explicit numerical schemes are unconditionally stable. Numerical solutions obtained from both schemes are compared. Initial curves with both zero and finite contact angles are considered....

By incorporating the higher-order concept with perfectly matched later (PML) scheme, unconditionally stable approximate Crank–Nicolson algorithm is proposed for plasma simulation in open region problems. More precisely, implementation based on CN Direct-Splitting (CNDS) procedure finite-difference time-domain (FDTD) unmagnetized simulation. The can be regarded as frequency-dependent media which...

In the article, a differential scheme is created for first-order diffusion equation using Crank-Nicolson method. The stability of was checked Neumann To solve problem numerically, intervals were found Neman This work presents an analysis two-dimensional Von analysis. widely used numerical method solving partial equations that combines explicit and implicit schemes. important factor to consider ...

Numerical solution methods for pricing American options are considered. We propose a second-order accurate Runge-Kutta scheme for the time discretization of the Black-Scholes partial differential equation with an early exercise constraint. We reformulate the algorithm introduced by Brennan and Schwartz into a simple form using a LU decomposition and a modified backward substitution with a proje...

The time dependent Ginzburg-Landau (TDGL) equation is a typical model in phase field theory for many applications like two phase flow simulations and phase transitions. In this paper, we develop effective algorithms so that the solution of the TDGL model can be accurately approximated. Specifically, we adopt finite element methods for the spatial discretization and study different algorithms fo...

We consider an initial boundary value problem for a one-dimensional fractional-order parabolic equation with a space fractional derivative of Riemann–Liouville type and order α ∈ (1, 2). We study a spatial semidiscrete scheme using the standard Galerkin finite element method with piecewise linear finite elements, as well as fully discrete schemes based on the backward Euler method and the Crank...

We introduce a new structure preserving, second order in time relaxation-type scheme for approximating solutions of the Schr\"odinger-Poisson system. More specifically, we use Crank-Nicolson as stepping mechanism, whilst nonlinearity is handled by means relaxation approach spirit \cite{Besse, KK} nonlinear Schr\"odinger equation. For spatial discretisation standard conforming finite element sch...

The unsteady stagnation point flow and heat transfer with prescribed flux towards a stretching and shrinking sheet with viscous dissipation is studied. Similarity transformation is adopted to initially convert the governing differential equations into nonlinear ordinary differential equations. The two-point boundary value ordinary differential equations (ODE) are subsequently converted into par...

We consider numerical methods for solving the fractional-in-space Allen-Cahn (FiSAC) equation which contains small perturbation parameters and strong noninearilty. Standard fully discretized schemes for the the FiSAC equation will be considered, namely, in time the conventional first-order implicit-explicit scheme or second-order Crank-Nicolson scheme and in space a secondorder finite differenc...