An Operator Splitting Scheme for Biharmonic Equation with Accelerated Convergence

2006 ◽  
pp. 387-394 ◽  
Author(s):  
X. H. Tang ◽  
Ch. I. Christov
Keyword(s):  
Biharmonic Equation ◽  
Operator Splitting ◽  
Splitting Scheme ◽  
Accelerated Convergence

scholarly journals Operator splitting around Euler-Maruyama scheme and high order discretization of heat kernels

2020 ◽  
Author(s):  
Toshihiro Yamada ◽  
Yuga Iguchi
Keyword(s):  
Commutative Algebra ◽  
Computational Algorithm ◽  
Diffusion Processes ◽  
Operator Splitting ◽  
Heat Kernels ◽  
Heat Equations ◽  
Discretization Method ◽  
Splitting Scheme ◽  
Order Operator ◽  
Numerical Examples

This paper proposes a general higher order operator splitting scheme for diffusion semigroups using the Baker-Campbell-Hausdorff type commutator expansion of non-commutative algebra and the Malliavin calculus. An accurate discretization method for the fundamental solution of heat equations or the heat kernel is introduced with a new computational algorithm which will be useful for the inference for diffusion processes. The approximation is regarded as the splitting around the Euler-Maruyama scheme for the density. Numerical examples for diffusion processes are shown to validate the proposed scheme.

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