Improving the Laplace transform integration method

The Laplace transform method for Burgers’ equation

The Laplace transform method (LTM) is introduced to solve Burgers’ equation. Because of the nonlinear term in Burgers’ equation, one cannot directly apply the LTM. Increment linearization technique is introduced to deal with the situation. This is a key idea in this paper. The increment linearization technique is the following: In time level t , we divide the solution u(x, t) into two parts: u(...

Nonlinearities distribution Laplace transform-homotopy perturbation method

This article proposes non-linearities distribution Laplace transform-homotopy perturbation method (NDLT-HPM) to find approximate solutions for linear and nonlinear differential equations with finite boundary conditions. We will see that the method is particularly relevant in case of equations with nonhomogeneous non-polynomial terms. Comparing figures between approximate and exact solutions we ...

Inverse Laplace transform method for multiple solutions of the fractional Sturm-Liouville problems

In this paper, inverse Laplace transform method is applied to analytical solution of the fractional Sturm-Liouville problems. The method introduces a powerful tool for solving the eigenvalues of the fractional Sturm-Liouville problems. The results  how that the simplicity and efficiency of this method.

Laplace Transform

We have seen before that Fourier analysis is very useful in the study of signals and linear and time invariant (LTI) systems. The main reason is that a lot of signals can be expressed as a linear combination of complex exponentials of the form e with s = jw. There are many properties that still apply when s is not restricted to be pure imaginary. That is why we introduce a generalization of the...

Solving Fuzzy Integral Equations of the Second Kind by Fuzzy Laplace Transform Method