scholarly journals A positivity-preserving, energy stable and convergent numerical scheme for the Poisson-Nernst-Planck system

2021 ◽  
pp. 1 ◽  
Author(s):  
Chun Liu ◽  
Cheng Wang ◽  
Steven M. Wise ◽  
Xingye Yue ◽  
Shenggao Zhou
Keyword(s):  
Numerical Scheme ◽  
Positivity Preserving ◽  
Energy Stable

A Uniquely Solvable, Energy Stable Numerical Scheme for the Functionalized Cahn–Hilliard Equation and Its Convergence Analysis

2018 ◽  
Vol 76 (3) ◽  
pp. 1938-1967 ◽  
Author(s):  
Wenqiang Feng ◽  
Zhen Guan ◽  
John Lowengrub ◽  
Cheng Wang ◽  
Steven M. Wise ◽  
...  
Keyword(s):  
Convergence Analysis ◽  
Numerical Scheme ◽  
Hilliard Equation ◽  
Energy Stable ◽  
Cahn Hilliard Equation

A new numerical scheme for the CIR process

2015 ◽  
Vol 21 (3) ◽  
Author(s):  
Nikolaos Halidias
Keyword(s):  
Numerical Scheme ◽  
Order Of Convergence ◽  
Positivity Preserving ◽  
Cir Process ◽  
Well Posed

AbstractIn this paper we generalize an explicit numerical scheme for the CIR process that we have proposed before. The advantage of the new proposed scheme is that preserves positivity and is well posed for a (little bit) broader set of parameters among the positivity preserving schemes. The order of convergence is at least logarithmic in general and for a smaller set of parameters is at least 1/4.

A family of positivity preserving schemes for numerical solution of Black–Scholes equation

2016 ◽  
Vol 03 (04) ◽  
pp. 1650025
Author(s):  
M. Mehdizadeh Khalsaraei ◽  
R. Shokri Jahandizi
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Exact Solution ◽  
Numerical Solution ◽  
Numerical Scheme ◽  
Initial Vector ◽  
Positivity Preserving ◽  
Fully Implicit ◽  
Black Scholes ◽  
Spurious Oscillations

When one solves the Black–Scholes partial differential equation, it is of great important that numerical scheme to be free of spurious oscillations and satisfy the positivity requirement. With positivity, we mean, the component non-negativity of the initial vector, is preserved in time for the exact solution. Numerically, such property for fully implicit scheme is not always satisfied by approximated solutions and they generate spurious oscillations in the presence of discontinuous payoff. In this paper, by using the nonstandard discretization strategy, we propose a new scheme that is free of spurious oscillations and satisfies the positivity requirement.

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