Numerical inversion of laplace transform via wavelet in partial differential equations

Hsiao, C. H.

doi:10.1002/num.21825

Cited by 7 publications

(2 citation statements)

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“…There exist a number of analytical and numerical methods for inverting a Laplace transform. For details one can refer [24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41]. The Laplace transform method reduces the differential or integral equation into a system of algebraic equations due to the Heaviside's operational method.…”

Section: Introductionmentioning

confidence: 99%

Numerical Inverse Laplace Transform for Solving a Class of Fractional Differential Equations

2019

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This paper discusses the applications of numerical inversion of the Laplace transform method based on the Bernstein operational matrix to find the solution to a class of fractional differential equations. By the use of Laplace transform, fractional differential equations are firstly converted to system of algebraic equations then the numerical inverse of a Laplace transform is adopted to find the unknown function in the equation by expanding it in a Bernstein series. The advantages and computational implications of the proposed technique are discussed and verified in some numerical examples by comparing the results with some existing methods. We have also combined our technique to the standard Laplace Adomian decomposition method for solving nonlinear fractional order differential equations. The method is given with error estimation and convergence criterion that exclude the validity of our method.

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Section: Introductionmentioning

confidence: 99%

Numerical Inverse Laplace Transform for Solving a Class of Fractional Differential Equations

2019

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“…For finding the solution of differential and integral equations, operational matrices have been developed of the polynomials such as Walsh operational matrices, block pulse operational matrices, generalized block pulse operational matrices, Haar wavelet, Legendre wavelet, Bernoulli wavlet operational matrix, Jacobi operational matrix, and Chebyshev wavelet operational matrices . These references show the good dimensions of adopting operational matrices.…”

Section: Introductionmentioning

confidence: 99%

Numerical inversion of Laplace transform based on Bernstein operational matrix

Rani

Mishra

Cattani

2018

Math Methods in App Sciences

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This paper provides a technique to investigate the inverse Laplace transform by using orthonormal Bernstein operational matrix of integration. The proposed method is based on replacing the unknown function through a truncated series of Bernstein basis polynomials and the coefficients of the expansion are obtained using the operational matrix of integration. This is an alternative procedure to find the inversion of Laplace transform with few terms of Bernstein polynomials.Numerical tests on various functions have been performed to check the applicability and efficiency of the technique. The root mean square error between exact and numerical results is computed, which shows that the method produces the satisfactory results. A rough upper bound for errors is also estimated. KEYWORDSLaplace transform, numerical inverse Laplace transform, operational matrices, orthonormal Bernstein polynomialswhere c is a positive real number and all the poles of F(s) lie at the left side of the line s = c. Sometimes, inverse Laplace transform becomes complicated when the analytic inverse cannot be found. Hence, to calculate the inverse Laplace transform, numerical techniques are adopted.Recently, numerous different methods have been adopted for analytically and numerically inverting the Laplace transform, which is well suited to different types of functions. Lee and Sheen 5 developed analytic continuation of Bromwich integral and determined the integral by using quadrature rule, Dubner and Abate 6 expressed the function in Fourier cosine series, further it was improved by Durbin 7 that the trapezoidal rule can be applied and the function can be expressed in trigonometric series, Iqbal 8 studied the regularization method, Cuomo et al 9 have described a numerical technique based Math Meth Appl Sci. 2018;41:9231-9243.wileyonlinelibrary.com/journal/mma

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Parameter Identification Inverse Problems of Partial Differential Equations Based on the Improved Gene Expression Programming

Chen

2016

Lecture Notes in Computer Science

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Numerical inversion of laplace transform via wavelet in partial differential equations

Cited by 7 publications

References 16 publications

Numerical Inverse Laplace Transform for Solving a Class of Fractional Differential Equations

Numerical Inverse Laplace Transform for Solving a Class of Fractional Differential Equations

Numerical inversion of Laplace transform based on Bernstein operational matrix

Parameter Identification Inverse Problems of Partial Differential Equations Based on the Improved Gene Expression Programming

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