scholarly journals Branch Cuts of Stokes Wave on Deep Water. Part I: Numerical Solution and Padé Approximation

2016 ◽  
Vol 137 (4) ◽  
pp. 419-472 ◽  
Author(s):  
S. A. Dyachenko ◽  
P. M. Lushnikov ◽  
A. O. Korotkevich
Keyword(s):  
Numerical Solution ◽  
Deep Water ◽  
Padé Approximation ◽  
Stokes Wave ◽  
Pade Approximation ◽  
Branch Cuts ◽  
Deep Water Part

scholarly journals Approximate Solution of Riccati Differential Equation via Modified Greens Decomposition Method

2020 ◽  
Vol 70 (4) ◽  
pp. 419-424
Author(s):  
Amit Ujlayan ◽  
Mohit Arya
Keyword(s):  
Numerical Solution ◽  
Decomposition Method ◽  
Padé Approximation ◽  
Medical Science ◽  
Adomian Decomposition Method ◽  
Specific Class ◽  
Pade Approximation ◽  
Riccati Differential Equation ◽  
Adomian Polynomials ◽  
Adomian Decomposition

Riccati differential equations (RDEs) plays important role in the various fields of defence, physics, engineering, medical science, and mathematics. A new approach to find the numerical solution of a class of RDEs with quadratic nonlinearity is presented in this paper. In the process of solving the pre-mentioned class of RDEs, we used an ordered combination of Green’s function, Adomian’s polynomials, and Pade` approximation. This technique is named as green decomposition method with Pade` approximation (GDMP). Since, the most contemporary definition of Adomian polynomials has been used in GDMP. Therefore, a specific class of Adomian polynomials is used to advance GDMP to modified green decomposition method with Pade` approximation (MGDMP). Further, MGDMP is applied to solve some special RDEs, belonging to the considered class of RDEs, absolute error of the obtained solution is compared with Adomian decomposition method (ADM) and Laplace decomposition method with Pade` approximation (LADM-Pade`). As well, the impedance of the method emphasised with the comparative error tables of the exact solution and the associated solutions with respect to ADM, LADM-Pade`, and MGDMP. The observation from this comparative study exhibits that MGDMP provides an improved numerical solution in the given interval. In spite of this, generally, some of the particular RDEs (with variable coefficients) cannot be easily solved by some of the existing methods, such as LADM-Pade` or Homotopy perturbation methods. However, under some limitations, MGDMP can be successfully applied to solve such type of RDEs.

Algorithms for Solving the Catch Equation Forward and Backward in Time

1982 ◽  
Vol 39 (1) ◽  
pp. 197-202 ◽  
Author(s):  
S. E. Sims
Keyword(s):  
Mortality Rate ◽  
Numerical Solution ◽  
Exponential Function ◽  
Newton’S Method ◽  
Newton's Method ◽  
Padé Approximation ◽  
Approximate Solutions ◽  
Fishing Mortality ◽  
Convergence Criteria ◽  
Pade Approximation

Approximate solutions to the catch equation for the fishing mortality rate both forward and backward in time are obtained with an application of the diagonal Padé approximation of degree four to the exponential function. In either case the resulting approximation as well as Pope's estimate are shown to serve quite well as starting values for Newton's Method which is used to obtain a numerical solution of the catch equation. Convergence criteria for Newton's Method are discussed in each setting.Key words: catch equation, Newton's method, Padé approximation, Pope's estimate

scholarly journals The Numerical Method for Solving Differential Equations of Lane-Emden Type by Padé Approximation

2011 ◽  
Vol 2011 ◽  
pp. 1-9 ◽  
Author(s):  
Muhammed Yiğider ◽  
Khatereh Tabatabaei ◽  
Ercan Çelik
Keyword(s):  
Differential Equation ◽  
Power Series ◽  
Differential Equations ◽  
Numerical Solution ◽  
Numerical Method ◽  
Padé Approximation ◽  
Pade Approximation ◽  
One Dimensional ◽  
Series Form ◽  
Differential Transformation

Numerical solution differential equation of Lane-Emden type is considered by Padé approximation. We apply these method to two examples. First differential equation of Lane-Emden type has been converted to power series by one-dimensional differential transformation, then the numerical solution of equation was put into Padé series form. Thus, we have obtained numerical solution differential equation of Lane-Emden type.

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