scholarly journals A Study on the Applications of Laplace Transformation

2021 ◽  
Vol 23 (08) ◽  
pp. 84-91
Author(s):  
Gagan Gaba ◽  
Keyword(s):  
Differential Equations ◽  
Laplace Transform ◽  
Everyday Life ◽  
Integral Equations ◽  
Laplace Transformation ◽  
Real Life ◽  
Laplace Transforms ◽  
Life Problems ◽  
Research Problems

Mathematics plays an important role in our everyday life. Laplace transform is one of the important tools which is used by researchers to find the solutions of various real life problems modeled into differential equations or simultaneous differential equations or Integral equations. In this paper, we are going to study the details on lapace transform, its properties and “Applications of Laplace Transform in Various Fields”. Various uses of Laplace Transforms in the research problems have been highlighted. Detailed applications of Laplace Transform have been discussed.

scholarly journals SOLVING SYSTEMS OF FRACTIONAL PARTIAL DIFFERENTIAL EQUATIONS VIA TWO DIMENSIONAL LAPLACE TRANSFORMS

2020 ◽  
Vol 5 (12) ◽  
pp. 406-420
Author(s):  
A. Aghili ◽  
M.R. Masomi
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Laplace Transform ◽  
Laplace Transforms ◽  
Heat Equations ◽  
Two Dimensional ◽  
Fractional Partial Differential Equations ◽  
Partial Differential ◽  
Homogeneous Systems ◽  
Fractional Pde

In this article, the authors used two dimensional Laplace transform to solve non - homogeneous sub - ballistic fractional PDE and homogeneous systems of time fractional heat equations. Constructive examples are also provided.

scholarly journals Convergence and Stability Results of Modified CUIA Iterative Scheme for Hyperbolic Convex Metric space

2021 ◽  
Vol 2089 (1) ◽  
pp. 012040
Author(s):  
Surjeet Singh Chauhan Gonder ◽  
Khushboo Basra
Keyword(s):  
Fixed Points ◽  
Integral Equations ◽  
Metric Space ◽  
Iterative Scheme ◽  
Real Life ◽  
Convex Metric Space ◽  
Convergence And Stability ◽  
Life Problems ◽  
Stability Results ◽  
Differential And Integral Equations

Abstract The iterative fixed points have numerous applications in locating the solution of some real-life problems which can be modelled into linear as well as nonlinear differential and integral equations. In this manuscript, first of all, a new iterative scheme namely Modified CUIA iterative scheme is introduced. We first prove a theorem to check the convergence of this iteration for Hyperbolic Convex metric space. The result is then supported with one example. Further, another theorem is proved establishing the weak T stability of modified CUIA iterative scheme on the above space.

scholarly journals A Review on a Class of Second Order Nonlinear Singular BVPs

Mathematics ◽  
2020 ◽  
Vol 8 (7) ◽  
pp. 1045
Author(s):  
Amit K. Verma ◽  
Biswajit Pandit ◽  
Lajja Verma ◽  
Ravi P. Agarwal
Keyword(s):  
Exact Solution ◽  
Differential Equations ◽  
Real Life ◽  
Monotone Iterative Technique ◽  
Singular Boundary ◽  
Singular Boundary Value Problems ◽  
Numerical Techniques ◽  
Singular Differential Equations ◽  
Monotone Iterative ◽  
Life Problems

Several real-life problems are modeled by nonlinear singular differential equations. In this article, we study a class of nonlinear singular differential equations, explore its various aspects, and provide a detailed literature survey. Nonlinear singular differential equations are not easy to solve and their exact solution does not exist in most cases. Since the exact solution does not exist, it is natural to look for the existence of the analytical solution and numerical solution. In this survey, we focus on both aspects of nonlinear singular boundary value problems (SBVPs) and cover different analytical and numerical techniques which are developed to deal with a class of nonlinear singular differential equations − ( p ( x ) y ′ ( x ) ) ′ = q ( x ) f ( x , y , p y ′ ) for x ∈ ( 0 , b ) , subject to suitable initial and boundary conditions. The monotone iterative technique has also been briefed as it gained a lot of attention during the last two decades and it has been merged with most of the other existing techniques. A list of SBVPs is also provided which will be of great help to researchers working in this area.

scholarly journals Laplace transforms and the American straddle

2002 ◽  
Vol 2 (3) ◽  
pp. 121-129 ◽  
Author(s):  
G. Alobaidi ◽  
R. Mallier
Keyword(s):  
Laplace Transform ◽  
Integral Equations ◽  
Laplace Transforms ◽  
Dividend Yield

We address the pricing of American straddle options. We use partial Laplace transform techniques due to Evans et al. (1950) to derive a pair of integral equations giving the locations of the optimal exercise boundaries for an American straddle option with a constant dividend yield.

scholarly journals Sinc Based Inverse Laplace Transforms, Mittag-Leffler Functions and Their Approximation for Fractional Calculus

2021 ◽  
Vol 5 (2) ◽  
pp. 43
Author(s):  
Gerd Baumann
Keyword(s):  
Differential Equations ◽  
Fractional Calculus ◽  
Laplace Transform ◽  
Fractional Differential Equations ◽  
Numerical Approximation ◽  
Laplace Transforms ◽  
Inverse Laplace Transform ◽  
Exact Methods ◽  
Sinc Methods ◽  
Fractional Differential

We shall discuss three methods of inverse Laplace transforms. A Sinc-Thiele approximation, a pure Sinc, and a Sinc-Gaussian based method. The two last Sinc related methods are exact methods of inverse Laplace transforms which allow us a numerical approximation using Sinc methods. The inverse Laplace transform converges exponentially and does not use Bromwich contours for computations. We apply the three methods to Mittag-Leffler functions incorporating one, two, and three parameters. The three parameter Mittag-Leffler function represents Prabhakar’s function. The exact Sinc methods are used to solve fractional differential equations of constant and variable differentiation order.

scholarly journals Formulative Visualization of Numerical Methods for Solving Non-Linear Ordinary Differential Equations

2021 ◽  
Vol 2 (2) ◽  
pp. 79-88
Author(s):  
Jeevan Kafle ◽  
Bhogendra Kumar Thakur ◽  
Grishma Acharya
Keyword(s):  
Numerical Methods ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Real Life ◽  
Euler Method ◽  
Linear Ordinary Differential Equations ◽  
Life Problems ◽  
Backward Euler ◽  
Non Linear ◽  
Runge Kutta

Many physical problems in the real world are frequently modeled by ordinary differential equations (ODEs). Real-life problems are usually non-linear, numerical methods are therefore needed to approximate their solution. We consider different numerical methods viz., Explicit (Forward) and Implicit (Backward) Euler method, Classical second-order Runge-Kutta (RK2) method (Heun’s method or Improved Euler method), Third-order Runge-Kutta (RK3) method, Fourth-order Runge-Kutta (RK4) method, and Butcher fifth-order Runge-Kutta (BRK5) method which are popular classical iteration methods of approximating solutions of ODEs. Moreover, an intuitive explanation of those methods is also be presented, comparing among them and also with exact solutions with necessary visualizations. Finally, we analyze the error and accuracy of these methods with the help of suitable mathematical programming software.

scholarly journals Approximate Solution of Systems of Volterra Integral Equations of Second Kind by Adomian Decomposition Method

2015 ◽  
Vol 63 (1) ◽  
pp. 15-18
Author(s):  
Md Shariful Islam ◽  
Mir Shariful Islam ◽  
Md Zavid Iqbal Bangalee ◽  
AFM Khodadad Khan ◽  
Amal Halder
Keyword(s):  
Approximate Solution ◽  
Linear System ◽  
Integral Equations ◽  
Decomposition Method ◽  
Real Life ◽  
Adomian Decomposition Method ◽  
Volterra Integral Equations ◽  
Life Problems ◽  
Adomian Decomposition ◽  
Differential And Integral Equations

Real life problems that arise in different branches of science and social science, in the form of differential and integral equations are non-linear in nature. However, methods developed in Mathematics, usually, are suitable for the linear system. In this article, we talk on approximating solution of system of Volterra integral equations of second kind in an analytic way using Adomian decomposition method in Mathematica. DOI: http://dx.doi.org/10.3329/dujs.v63i1.21761 Dhaka Univ. J. Sci. 63(1): 15-18, 2015 (January)

Equivalence of History-Function Based and Infinite-Dimensional-State Initializations for Fractional-Order Operators

2013 ◽  
Vol 8 (4) ◽  
Author(s):  
Tom T. Hartley ◽  
Carl F. Lorenzo ◽  
Jean-Claude Trigeassou ◽  
Nezha Maamri
Keyword(s):  
Differential Equations ◽  
Laplace Transform ◽  
State Space ◽  
Fractional Order ◽  
Laplace Transforms ◽  
Space Representation ◽  
Infinite Dimensional ◽  
State Space Representation ◽  
Fractional Order Differential Equations ◽  
Dimensional State Space

Proper initialization of fractional-order operators has been an ongoing problem, particularly in the application of Laplace transforms with correct initialization terms. In the last few years, a history-function-based initialization along with its corresponding Laplace transform has been presented. Alternatively, an infinite-dimensional state-space representation along with its corresponding Laplace transform has also been presented. The purpose of this paper is to demonstrate that these two approaches to the initialization problem for fractional-order operators are equivalent and that the associated Laplace transforms yield the correct initialization terms and can be used in the solution of fractional-order differential equations.

scholarly journals Approximating non linear higher order ODEs by a three point block algorithm

PLoS ONE ◽  
2021 ◽  
Vol 16 (2) ◽  
pp. e0246904
Author(s):  
Ahmad Fadly Nurullah Rasedee ◽  
Mohammad Hasan Abdul Sathar ◽  
Khairil Iskandar Othman ◽  
Siti Raihana Hamzah ◽  
Norizarina Ishak
Keyword(s):  
Numerical Methods ◽  
Differential Equations ◽  
Numerical Algorithm ◽  
Computational Cost ◽  
Real Life ◽  
Higher Order ◽  
Multistep Method ◽  
Stability And Convergence ◽  
Block Algorithm ◽  
Life Problems

Differential equations are commonly used to model various types of real life applications. The complexity of these models may often hinder the ability to acquire an analytical solution. To overcome this drawback, numerical methods were introduced to approximate the solutions. Initially when developing a numerical algorithm, researchers focused on the key aspect which is accuracy of the method. As numerical methods becomes more and more robust, accuracy alone is not sufficient hence begins the pursuit of efficiency which warrants the need for reducing computational cost. The current research proposes a numerical algorithm for solving initial value higher order ordinary differential equations (ODEs). The proposed algorithm is derived as a three point block multistep method, developed in an Adams type formulae (3PBCS) and will be used to solve various types of ODEs and systems of ODEs. Type of ODEs that are selected varies from linear to nonlinear, artificial and real life problems. Results will illustrate the accuracy and efficiency of the proposed three point block method. Order, stability and convergence of the method are also presented in the study.

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