scholarly journals Complete Response of Linear Circuits to Periodic Nonsinusoidal Input in MATLAB

2020 ◽  
Vol 5 (3) ◽  
pp. 70-74
Author(s):  
Iveta Tomčíková
Keyword(s):  
Laplace Transform ◽  
Complete Response ◽  
Complex Frequency ◽  
Analysis Technique ◽  
Periodic Input ◽  
The Laplace Transform ◽  
Linear Circuits ◽  
The Given

The paper deals with the proposal for finding<br />the complete response of dynamic linear circuits to a<br />periodic nonsinusoidal input in the MATLAB environment.<br />A very powerful tool for solving the given problem is to<br />transform the circuits directly into the complex frequency<br />domain using the Laplace transform and then apply the<br />sparse tableau analysis technique to solve them. Applying<br />above-mentioned methods in the MATLAB environment, it<br />is not difficult to find the complete response of dynamic<br />linear circuits to the periodic input.

scholarly journals Analytical Analysis of Fractional-Order Physical Models via a Caputo-Fabrizio Operator

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Fatemah Mofarreh ◽  
A. M. Zidan ◽  
Muhammad Naeem ◽  
Rasool Shah ◽  
Roman Ullah ◽  
...  
Keyword(s):  
Laplace Transform ◽  
Fractional Order ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Physical Models ◽  
Heat Equations ◽  
Transform Method ◽  
Adomian Decomposition ◽  
The Laplace Transform ◽  
The Given

This paper investigates a modified analytical method called the Adomian decomposition transform method for solving fractional-order heat equations with the help of the Caputo-Fabrizio operator. The Laplace transform and the Adomian decomposition method are implemented to obtain the result of the given models. The validity of the proposed method is verified by considering some numerical problems. The solution achieved has shown that the better accuracy of the suggested method. Furthermore, due to the straightforward implementation, the proposed method can solve other nonlinear fractional-order problems.

Quaternion domain Laplace transform of the pulse vector

2021 ◽  
Author(s):  
V.M. Sovetov
Keyword(s):  
Laplace Transform ◽  
Transfer Functions ◽  
Mimo Systems ◽  
Matrix Multiplication ◽  
Time Shift ◽  
Complex Frequency ◽  
Hypercomplex Numbers ◽  
Radio Engineering ◽  
The Matrix ◽  
The Laplace Transform

The Laplace transform (LT) is widely used in radio engineering for signal and circuit analysis. The PL greatly facilitates the solution of differential equations, the calculation of transfer functions, the finding of impulse responses, etc. Multiple-Input Multiple-Output (MIMO) systems are becoming more common today. With input influences on such systems, at the output signals are obtained, the elements of which are closely related to each other, and changes in some influencing elements of the input vector change the values of others. Such changes are usually associated with the preservation of the vector norm during transformation. Obviously, this completely changes the shape of the output response and, accordingly, its spectrum. To calculate such changes, it is possible to use the usual PL of real signals and the corresponding theorems. However, this approach requires a significant investment of time and computational resources. If you change the amplitude, shape, time shift of at least one pulse, you will have to repeat all the calculations again. Quaternion transformations, including the Laplace transform, have been studied in many works. However, these studies are often of a general theoretical nature or are used only to obtain the Fractional Quaternion Laplace Transform of 2D images. To calculate the LT of the impulse vector when using the MIMO scheme, it is proposed to use hypercomplex numbers, in the particular case, quaternions. Quaternion is a hypercomplex number with one scalar and three imaginary numbers i, j, k. To get rid of operations with imaginary numbers, the quaternion is represented as an orthogonal 4×4 matrix. The matrix, in turn, is decomposed into 4 basis matrices. Moreover, operations with matrices correspond to operations with imaginary units and the quaternion as a whole. It is shown that the quaternionic Laplace transform (QLT) of the vector is represented as a one-dimensional integral from 0 to ∞ of the vector. In this case, the matrix exponent in the power of the quaternion frequency matrix S = Eσ + 1/√3(I + J + K)ω is used as the transformation kernel, where E, I, J, K are basis matrices. The main properties of the QLT are considered. It is shown that in terms of the notation form, the properties of the QLT correspond to the properties of the LT of real functions, taking into account the non-commutativity of matrix multiplication. Therefore, to calculate the QLT, it is possible to use the well-known expressions for the LT of real pulses with the replacement of the complex frequency s by the matrix of quaternion frequencies S. Expressions for the QLT are obtained for the pulse vectors, which are often used to solve radio engineering problems. It is shown that for σ = 0 these expressions correspond to the quaternionic Fourier transform of the vector pulses. In general, vector pulses can have different delays, amplitudes and shapes. Expressions are obtained for finding the QLT of such vectors.

scholarly journals Numerical Solution of Fractional-Order Fredholm Integrodifferential Equation in the Sense of Atangana–Baleanu Derivative

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Jian Wang ◽  
Kamran ◽  
Ayesha Jamal ◽  
Xuemei Li
Keyword(s):  
Laplace Transform ◽  
Integrodifferential Equation ◽  
Numerical Scheme ◽  
High Accuracy ◽  
Trapezoidal Rule ◽  
Inverse Laplace Transform ◽  
Fredholm Type ◽  
The Laplace Transform ◽  
Linear And Nonlinear ◽  
The Given

In the present article, our aim is to approximate the solution of Fredholm-type integrodifferential equation with Atangana–Baleanu fractional derivative in Caputo sense. For this, we propose a method based on Laplace transform and inverse LT. In our numerical scheme, the given equation is transformed to an algebraic equation by employing the Laplace transform. The reduced equation will be solved in complex plane. Finally, the solution of the given problem is obtained via inverse Laplace transform by representing it as a contour integral. Then, the trapezoidal rule is used to approximate the integral to high accuracy. We have considered linear and nonlinear fractional Fredholm integrodifferential equations to validate our method.

The extinction time of a general birth and death process with catastrophes

1986 ◽  
Vol 23 (04) ◽  
pp. 851-858 ◽  
Author(s):  
P. J. Brockwell
Keyword(s):  
Laplace Transform ◽  
Size Distribution ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Death Process ◽  
Extinction Time ◽  
Birth And Death Process ◽  
Different Types ◽  
The Laplace Transform ◽  
Necessary And Sufficient

The Laplace transform of the extinction time is determined for a general birth and death process with arbitrary catastrophe rate and catastrophe size distribution. It is assumed only that the birth rates satisfyλ0= 0,λj&gt; 0 for eachj&gt; 0, and. Necessary and sufficient conditions for certain extinction of the population are derived. The results are applied to the linear birth and death process (λj=jλ, µj=jμ) with catastrophes of several different types.

The Resolvent Operator

2017 ◽  
Author(s):  
Charles L. Epstein ◽  
Rafe Mazzeo
Keyword(s):  
Cauchy Problem ◽  
Heat Equation ◽  
Laplace Transform ◽  
Heat Kernel ◽  
Resolvent Operator ◽  
Contour Integration ◽  
Resolvent Kernel ◽  
The Laplace Transform ◽  
Elliptic Estimates ◽  
The Resolvent Operator

This chapter describes the construction of a resolvent operator using the Laplace transform of a parametrix for the heat kernel and a perturbative argument. In the equation (μ‎-L) R(μ‎) f = f, R(μ‎) is a right inverse for (μ‎-L). In Hölder spaces, these are the natural elliptic estimates for generalized Kimura diffusions. The chapter first constructs the resolvent kernel using an induction over the maximal codimension of bP, and proves various estimates on it, along with corresponding estimates for the solution operator for the homogeneous Cauchy problem. It then considers holomorphic semi-groups and uses contour integration to construct the solution to the heat equation, concluding with a discussion of Kimura diffusions where all coefficients have the same leading homogeneity.

scholarly journals Algebraic inversion of the Laplace transform

2005 ◽  
Vol 50 (1-2) ◽  
pp. 179-185 ◽  
Author(s):  
P.G. Massouros ◽  
G.M. Genin
Keyword(s):  
Laplace Transform ◽  
The Laplace Transform

scholarly journals Approximation of linear one dimensional partial differential equations including fractional derivative with non-singular kernel

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Raheel Kamal ◽  
Kamran ◽  
Gul Rahmat ◽  
Ali Ahmadian ◽  
Noreen Izza Arshad ◽  
...  
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Laplace Transform ◽  
Fractional Derivative ◽  
Meshless Method ◽  
Inverse Laplace Transform ◽  
Contour Integral ◽  
Partial Differential ◽  
One Dimensional ◽  
The Laplace Transform

AbstractIn this article we propose a hybrid method based on a local meshless method and the Laplace transform for approximating the solution of linear one dimensional partial differential equations in the sense of the Caputo–Fabrizio fractional derivative. In our numerical scheme the Laplace transform is used to avoid the time stepping procedure, and the local meshless method is used to produce sparse differentiation matrices and avoid the ill conditioning issues resulting in global meshless methods. Our numerical method comprises three steps. In the first step we transform the given equation to an equivalent time independent equation. Secondly the reduced equation is solved via a local meshless method. Finally, the solution of the original equation is obtained via the inverse Laplace transform by representing it as a contour integral in the complex left half plane. The contour integral is then approximated using the trapezoidal rule. The stability and convergence of the method are discussed. The efficiency, efficacy, and accuracy of the proposed method are assessed using four different problems. Numerical approximations of these problems are obtained and validated against exact solutions. The obtained results show that the proposed method can solve such types of problems efficiently.

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