An unconditionally stable andO(?2 +h4) orderL? convergent difference scheme for linear parabolic equations with variable coefficients

2001 ◽  
Vol 17 (6) ◽  
pp. 619-631 ◽  
Author(s):  
Zhi-Zhong Sun
Keyword(s):  
Difference Scheme ◽  
Parabolic Equations ◽  
Variable Coefficients ◽  
Unconditionally Stable ◽  
Linear Parabolic Equations ◽  
Convergent Difference Scheme

An Unconditionally Stable and High-Order Convergent Difference Scheme for Stokes’ First Problem for a Heated Generalized Second Grade Fluid with Fractional Derivative

2017 ◽  
Vol 10 (3) ◽  
pp. 597-613 ◽  
Author(s):  
Cuicui Ji ◽  
Zhizhong Sun
Keyword(s):  
Fractional Derivative ◽  
Difference Scheme ◽  
Second Order ◽  
Second Grade ◽  
Second Grade Fluid ◽  
Unconditionally Stable ◽  
Grade Fluid ◽  
Generalized Second Grade Fluid ◽  
Second Order Convergence ◽  
Convergent Difference Scheme

AbstractThis article is intended to fill in the blank of the numerical schemes with second-order convergence accuracy in time for nonlinear Stokes’ first problem for a heated generalized second grade fluid with fractional derivative. A linearized difference scheme is proposed. The time fractional-order derivative is discretized by second-order shifted and weighted Gr¨unwald-Letnikov difference operator. The convergence accuracy in space is improved by performing the average operator. The presented numerical method is unconditionally stable with the global convergence order of in maximum norm, where τ and h are the step sizes in time and space, respectively. Finally, numerical examples are carried out to verify the theoretical results, showing that our scheme is efficient indeed.

scholarly journals Smoothing properties in multistep backward difference method and time derivative approximation for linear parabolic equations

2005 ◽  
Vol 2005 (4) ◽  
pp. 523-536
Author(s):  
Yubin Yan
Keyword(s):  
Difference Method ◽  
Parabolic Equations ◽  
Parabolic Problem ◽  
Approximation Scheme ◽  
Time Derivative ◽  
Nonsmooth Data ◽  
Smoothing Property ◽  
Linear Parabolic Equations ◽  
Linear Parabolic Problem ◽  
Data Error

A smoothing property in multistep backward difference method for a linear parabolic problem in Hilbert space has been proved, where the operator is selfadjoint, positive definite with compact inverse. By using the solutions computed by a multistep backward difference method for the parabolic problem, we introduce an approximation scheme for time derivative. The nonsmooth data error estimate for the approximation of time derivative has been obtained.

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