Numerical Schemes for Stochastic Differential Equation Models

2008 ◽  
Author(s):  
Desmond J. Higham ◽  
Peter E. Kloeden
Keyword(s):  
Differential Equation ◽  
Stochastic Differential Equation ◽  
Numerical Schemes ◽  
Differential Equation Models

Some stochastic differential equation models of an aquatic ecosystem

1978 ◽  
Vol 4 (1) ◽  
pp. 3-27 ◽  
Author(s):  
Jawahar Lal Tiwari ◽  
John E. Hobbie ◽  
James P. Reed ◽  
Donald W. Stanley ◽  
Michael C. Miller
Keyword(s):  
Differential Equation ◽  
Stochastic Differential Equation ◽  
Aquatic Ecosystem ◽  
Differential Equation Models

On the theory and application of one-step numerical schemes for solving quantum stochastic differential equation (QSDE)

2014 ◽  
Vol 07 (03) ◽  
pp. 1450037
Author(s):  
T. O. Akinwumi ◽  
B. J. Adegboyegun
Keyword(s):  
Differential Equation ◽  
Exact Solution ◽  
Stochastic Differential Equation ◽  
Numerical Experiments ◽  
Numerical Schemes ◽  
Quantum Stochastic Differential Equation ◽  
One Step ◽  
Definition Of ◽  
Convergent Sequences ◽  
Solution Techniques

This paper presents one-step numerical schemes for solving quantum stochastic differential equation (QSDE). The algorithms are developed based on the definition of QSDE and the solution techniques yield rapidly convergent sequences which are readily computable. As well as developing the schemes, we perform some numerical experiments and the solutions obtained compete favorably with exact solutions. The solution techniques presented in this work can handle all class of QSDEs most especially when the exact solution does not exist.

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