Approximating Convolution Integrals for Laplace and Exponential Fourier Transformations Using Simpson's Rule

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Approximating Convolution Integrals for Laplace and Exponential Fourier Transformations Using Simpson's Rule

In this thesis, we will explore approximating convolution integrals for Laplace and exponential Fourier transformations. For Laplace transforms, we will use the composite Simpson's Rule to make approximations firstly for convolutions with known results to compare and provide validity and then again for some without known results. For the exponential Fourier type, we first use the composite Simpson's Rule on a known result using different methods (two changes of variable and truncation) and compare to the known results to validate using the methods for convolution integrals without known results. Then, we will compare all methods per integral together.

title: Approximating Convolution Integrals for Laplace and Exponential Fourier Transformations Using Simpson's Rule

creator: Marlana Hatcher

subject: Applied mathematics [0364] - primary

subject: Mathematics [0405]

description: In this thesis, we will explore approximating convolution integrals for Laplace and exponential Fourier transformations. For Laplace transforms, we will use the composite Simpson's Rule to make approximations firstly for convolutions with known results to compare and provide validity and then again for some without known results. For the exponential Fourier type, we first use the composite Simpson's Rule on a known result using different methods (two changes of variable and truncation) and compare to the known results to validate using the methods for convolution integrals without known results. Then, we will compare all methods per integral together.

contributor: Tennessee Technological University

date: 2020-04-16

type: text

publisher: Tennessee Technological University. Archives and Special Collections

language: English

rights: In Copyright

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