The Crank-Nicolson Scheme
A Note on Crank Nicolson Scheme for Burgers’ Equation
... Keywords: Hopf-Cole Transformation, Burgers’ Equation, Crank-Nicolson Scheme, Nonlinear Partial Differential Equations.. It also has a large variety of applications in modeling of wat[r] ...
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A General ADE -FDTD with Crank-Nicolson Scheme for the Simulation of Dispersive Structures
... with Crank-Nicolson Scheme for the Simulation of Dispersive Structures Shi-Yu Long, Wei-Jun Chen * , Qi-Wen Liang, and Min Zhao Abstract—A general auxiliary differential equation (ADE) finite difference ...
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Random Crank Nicolson Scheme for Random Heat Equation in Mean Square Sense
... random Crank-Nicolson solution for heat equation con- taining uncertainty through the ...random Crank-Nicolson solution is satisfying mean square convergent through the whole ...random ...
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Optimal Error Estimates of the Crank Nicolson Scheme for Solving a Kind of Decoupled FBSDEs
... ( 1 ) L p p ≥ sense are of high order convergence in solving y and z . In [9], the authors rigorously obtained the error estimate of Crank-Nicolson scheme for solving generalized BSDEs, and ...
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Barycentric interpolation collocation method based on Crank-Nicolson scheme for the Allen-Cahn equation
... numerical scheme for the Allen-Cahn equation that represents a phenomenological model for anti-phase domain coarsening in a binary ...semi-discretized scheme in space is shown to be consistent. The ...
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Unconditional Stability Analysis of the 3D-Radial Point Interpolation Method and Crank-Nicolson Scheme
... and Crank-Nicolson Scheme Hichem Naamen * and Taoufik Aguili Abstract—This paper provides the theoretical validation of the unconditional stability using the Von Neumann method for the radial point ...
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Stability and convergence of the Crank Nicolson scheme for a class of variable coefficient tempered fractional diffusion equations
... A Crank-Nicolson scheme catering to solving initial-boundary value problems of a class of variable-coefficient tempered fractional diffusion equations is ...the scheme is unconditionally stable ...
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Crank -Nicolson scheme for solving a system of singularly perturbed partial differential equations of parabolic type
... the Crank- Nicolson scheme to discretise time variable on a uniform mesh and standard central difference scheme on a Shishkin piecewise uniform mesh to discretise space variable is suggested ...
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High order conservative Crank Nicolson scheme for regularized long wave equation
... extrapolation technique, the scheme has the accuracy of O( τ 2 + h 4 ) without refined mesh. Conservations of discrete mass and discrete energy are discussed, and existence of the numerical solution is proved by ...
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A new parallel difference algorithm based on improved alternating segment Crank–Nicolson scheme for time fractional reaction–diffusion equation
... difference scheme for time fractional reaction–diffusion equation and construct a class of improved alternating segment Crank–Nicolson (IASC–N) difference ...classical Crank–Nicolson (C–N) ...
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Stability of a Crank-Nicolson Pressure Correction Scheme Based on Staggered Discretizations
... numerical scheme, based on a pressure correction technique, uses a Crank- Nicolson time discretization and a staggered space discretization relying on the Rannacher-Turek finite ...the ...
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A Crank–Nicolson linear difference scheme for a BBM equation with a time fractional nonlocal viscous term
... a Crank–Nicolson-L1 (C-N-L1) linear difference scheme for problems ...numerical scheme are rigorously ...ical scheme is ...combination scheme of a Crank–Nicolson ...
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An alternating segment Crank–Nicolson parallel difference scheme for the time fractional sub diffusion equation
... segment Crank–Nicolson (ASC-N) parallel difference scheme is proposed for the time fractional sub-diffusion equation, which consists of the classical Crank–Nicolson scheme, four ...
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2 Quarter-Sweep Crank-Nicolson Approximation Equations
... Keywords Quarter-Sweep Improving Modified Gauss-Seidel method; Black-Scholes PDE; Crank-Nicolson scheme. 1 Introduction Option is a derivative which gives its holder the right but no obligation to ...
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Crank Nicolson implicit method for the nonlinear Schrodinger Equation with variable coefficient
... the Crank-Nicolson implicit scheme for the numerical solution of nonlinear Schrodinger equation with variable coefficient is ...The Crank-Nicolson scheme is second order accurate ...
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The Solution of Instability Phenomenon Arising in Homogeneous Porous Media by Crank-Nicolson Finite Difference Method
... using Crank-Nicolson scheme of finite difference method and the solution has been compared with the numerical solution by Finite Element Method and Exact solution obtained by analytical ...
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A Closed-Form Solution for Two-Dimensional Diffusion Equation Using Crank-Nicolson Finite Difference Method
... In this paper a finite difference method for solving 2-dimensional diffusion equation is presented. The method employs Crank-Nicolson scheme to improve fi- nite difference formulation and its ...
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Analysis of metal oxide varistor arresters for protection of multiconductor transmission lines using unconditionally-stable Crank-Nicolson FDTD
... implicit Crank–Nicolson finite difference time domain method; then, the IEEE recommended surge arrester model is reviewed and implemented by means of a local implicit scheme, based on a set of ...
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An optimized finite difference Crank Nicolson iterative scheme for the 2D Sobolev equation
... OFDCNI scheme has fully second-order accuracy, is unconditionally stable and absolutely convergent, and is only built by the POD basis constituted with the classical FDCN solutions over the initial very short time ...
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Efficient Excitation of Waveguides in Crank-Nicolson FDTD
... In order to solve this problem with CN-FDTD an average-in-time operator is applied to the fields affected by the space derivatives in Maxwell’s curl equations, and all the derivative operators are replaced by the ...
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