The Role of High Precision Arithmetic in Calculating Numerical Laplace and Inverse Laplace Transforms  

作　　者：Zinovi Krougly Matt Davison Sid Aiyar 

机构地区：[1]Department of Applied Mathematics, Western University, London, Ontario, Canada

出　　处：《Applied Mathematics》2017年第4期562-589,共28页应用数学（英文）

摘　　要：In order to find stable, accurate, and computationally efficient methods for performing the inverse Laplace transform, a new double transformation approach is proposed. To validate and improve the inversion solution obtained using the Gaver-Stehfest algorithm, direct Laplace transforms are taken of the numerically inverted transforms to compare with the original function. The numerical direct Laplace transform is implemented with a composite Simpson’s rule. Challenging numerical examples involving periodic and oscillatory functions, are investigated. The numerical examples illustrate the computational accuracy and efficiency of the direct Laplace transform and its inverse due to increasing the precision level and the number of terms included in the expansion. It is found that the number of expansion terms and the precision level selected must be in a harmonious balance in order for correct and stable results to be obtained.In order to find stable, accurate, and computationally efficient methods for performing the inverse Laplace transform, a new double transformation approach is proposed. To validate and improve the inversion solution obtained using the Gaver-Stehfest algorithm, direct Laplace transforms are taken of the numerically inverted transforms to compare with the original function. The numerical direct Laplace transform is implemented with a composite Simpson’s rule. Challenging numerical examples involving periodic and oscillatory functions, are investigated. The numerical examples illustrate the computational accuracy and efficiency of the direct Laplace transform and its inverse due to increasing the precision level and the number of terms included in the expansion. It is found that the number of expansion terms and the precision level selected must be in a harmonious balance in order for correct and stable results to be obtained.

关 键 词：NUMERICAL LAPLACE TRANSFORM NUMERICAL LAPLACE TRANSFORM INVERSION Composite Simpson’s Rule Gaver-Stehfest Algorithm High Precision Computation 

分 类 号：O1[理学—数学]