Abstract
In the present paper, we consider a first-order exponential splitting method (or exponential Lie-Trotter splitting) and second order exponential splitting method (or exponential Strang splitting method) for the Cauchy problem. Then we compare the errors between Lie-Trotter splitting and Strang splitting by discretizing the space into N sub-intervals, and compute the convergence rate for both Lie-Trotter splitting and Strang splitting methods.
Highlights
Operator splitting methods are widely used for numerical solution of partial differential equations
Any exponential operator splitting method involving several compositions can be cast into the following form, m et(A+B) = eaitAebitB + O(tm+1)
With m = 1, a1 = 1, b1 = 1, or a1 = 0, a2 = 1, b1 = 1, b2 = 0 respectively, that is, the first numerical solution is given by u1 = eAteBtu0 or u1 = eBteAtu0 (6)
Summary
Operator splitting methods are widely used for numerical solution of partial differential equations. The idea behind an operator splitting method is to split the differential operator into sub-operator having simpler forms, to simplify the solution of the resulting sub-problems. Operator splitting is a popular technique for solving coupled systems of partial differential equations, since complex equation system maybe split into separate parts that are more simpler to get solution. We concentrate on two exponential splitting methods: Lie-Trotter splitting and strang splitting. Any exponential operator splitting method involving several compositions can be cast into the following form, m et(A+B) = eaitAebitB + O(tm+1). Strang splitting as second order splitting method for Cauchy problem and compare the results between the two methods. In VI, the results. and in VII our conclusions
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