Inversion of Integral Equation Using Laplace Transform

2021 ◽  
pp. 31-34
Author(s):  
Priyank Jain ◽  
Archana Lala
Keyword(s):  
Integral Equation ◽  
Laplace Transform

Comparison of Laplace transform, integral equation, and assumed modes approaches for piezo-patch control of beams

2005 ◽  
Author(s):  
Oe. Kayacik ◽  
J. C. Bruch, Jr. ◽  
J. M. Sloss ◽  
S. Adali ◽  
I. S. Sadek
Keyword(s):  
Integral Equation ◽  
Laplace Transform

scholarly journals A Distributional Identity for the Bivariate Brownian Bridge: A Nontensor Gaussian Field

2018 ◽  
Vol 2018 ◽  
pp. 1-6
Author(s):  
Xiaohui Ai
Keyword(s):  
Integral Equation ◽  
Laplace Transform ◽  
Fredholm Integral Equation ◽  
Brownian Bridge ◽  
Gaussian Field ◽  
Brownian Sheet

The bivariate Brownian bridge, a nontensor Gaussian Field, is defined by B(t1,t2)=W(t1,t2)W(1,1)=0=W(t1,t2)-t1t2W(1,1), where t1,t2∈I=[0,1] and W(t1,t2) is a Brownian sheet. We obtain a distributional identity, a consequence of the Karhunen-Loève expansion for the bivariate Brownian bridge by Fredholm integral equation and Laplace transform approach.

LAPLACE TRANSFORMS AND INSTALLMENT OPTIONS

2004 ◽  
Vol 14 (08) ◽  
pp. 1167-1189 ◽  
Author(s):  
GHADA ALOBAIDI ◽  
ROLAND MALLIER ◽  
A. STANLEY DEAKIN
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Integral Equation ◽  
Free Boundary ◽  
Asymptotic Analysis ◽  
Laplace Transform ◽  
Financial Security ◽  
Present Value ◽  
Lump Sum ◽  
A Free Boundary Problem

An installment option is a derivative financial security where the price is paid in installments instead of as a lump sum at the time of purchase. The valuation of these options involves a free boundary problem in that at each installment date, the holder of the derivative has the option of continuing to pay the premiums or allowing the contract to lapse, and the decision will depend upon whether the present value of the expected pay-off is greater or less than the present value of the remaining premiums. Using a model installment option where the premiums are paid continuously rather than on discrete dates, an integral equation is derived for the position of this free boundary by applying a partial Laplace transform to the underlying partial differential equation for the value of the security. Asymptotic analysis of this integral equation allows us to deduce the behavior of the free boundary close to expiry.

Dynamic T-Stress for a Mode-I Crack in an Infinite Elastic Plane

2006 ◽  
Vol 74 (2) ◽  
pp. 378-381 ◽  
Author(s):  
Xian-Fang Li
Keyword(s):  
Integral Equation ◽  
Laplace Transform ◽  
Fourier Transforms ◽  
Integral Equation Method ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Inverse Laplace Transform ◽  
Elastic Plane ◽  
Time Space ◽  
T Stress

An integral equation method is presented to determine dynamic elastic T-stress. Special attention is paid to a single crack in an infinite elastic plane subjected to impact loading. By using the Laplace and Fourier transforms, the associated initial-boundary value problem is transformed to a Fredholm integral equation. The dynamic T-stress in the Laplace transform domain can be expressed in terms of its solution. Moreover, an explicit expression for initial T-stress is derived in closed form. Numerically solving the resulting equation and performing the inverse Laplace transform, the transient response of T-stress is determined in the time space, and the response history of the T-stress is shown graphically. Results indicate that T-stress exhibits apparent transient characteristic.

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