The energy method has been used as the main tool for deciding on stability for initial-boundary-value problems. This chapter considers first-order hyperbolic systems with constant coefficients. Such problems can be solved by using the Laplace transform. However, the Laplace transform method is a ...
The Laplace transform is an integral transform perhaps second only to the Fourier transform in its utility in solving physical problems. The Laplace transform is particularly useful in solving linear ordinary differential equations such as those arising in the analysis of electronic circuits. The (...
the method usingLaplace transformsis particulary useful in finding the solution”,又说道“Of course the problem can be solved by a number of other methods; but the Laplace-transform method appeals especially to the engineering scientist in that it reduces all problems...
The Laplace transform is particularly useful in solving equations involving piecewise or recursively defined functions. It can be used to solve certain initial-value problems. Some initial-value problems that involve differential equations with nonconstant coefficients can also be solved with the method ...
Use the Laplace transform to solve the following initial value problem: y″+14y′+98y=δ(t−5), y(0)=0, y′(0)=0 Solving Initial Value Problems Using Laplace Transform Differential equations can be solved using the Laplace transform method. Using L...
The Laplace transform, named after the French mathematician and astronomer Pierre Simon Laplace, converts functions into different mathematical domains to solve otherwise intractable problems. He used a similar transform on his additions to the probability theory. It became popular after World War Two....
Laplace transform methods are especially useful in solving problems that involve piecewise-defined, periodic, or impulse functions. Example 8.7.3 Solve x′=y=3δ(t−π)y′=−x+6δ(t−2π)x(0)=1,y(0)=−1. Solution We proceed in the exact same manner as in the previous ...
UUse laplace transform to solvey″+4y′+6y=1+e−t,y(0)=0,y′(0)=0. Laplace transform: In the given equation, we have to use the concept of Laplace transform. In this problem, we use formulae like: ∗L{y″}=s2Y(s)−sy(0)−y′(0)∗L−1{1(...
3.Analytical solution in real space is found by using theLaplace transformand decomposition method for infinite and finite reservoirs.本文研究了分形油藏无限大地层和有界地层非牛顿幂律流渗流模型 ,利用拉氏变换和分解的方法求得了井底定流量生产无限大地层及有界地层 (包括封闭和定压地层 )五种情况非牛顿幂律...
Laplace Transform: Solution of Initial Value Problems 1. y'' - 2y' + 2y = e^{-t}; y(0) = 0, y'(0) = 1 2. y'' + 2y'+ y = 4 e^{-t}; y(0) = 2, y'(0) = -1 Solve the following nonhomogeneous ODE by Laplace transform: y'' - 3 y'...