Vellore Institute of Technology (VIT) is a private university located in&nbsp;Tamil Nadu, India. Founded in 1984, as Vellore Engineering College, the institution offers 20 undergraduate, 34 postgraduate, four integrated and four research programs. It has campuses in Vellore, Amravati, Bhopal and Chennai.

VIT is one of the top ranked private universities in India according to NIRF, THE and QS Rankings.&nbsp;Govt. of India has recognized&nbsp;VIT, Vellore as an&nbsp;Institution of Eminence. This has allowed VIT to take independent quality initiatives and move up in world ranking.

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VIT University

Adomain decomposition method is a powerful technique to solve nonlinear differential equations and nonlinear Integro-differential equations. This paper presents a novel way of computing Adomian polynomials for nonlinear terms occur in nonlinear differential equations through partial Bell polynomial function(subroutine) in SageMath software. The obtained Adomian polynomials is used to solve nonlinear integral equations and nonlinear Integro-differential equations by Laplace Adomian decomposition method through symbolic computation in SageMath software. © 2020 IAEME Publication. All rights reserved.

Mathematics

School of Advanced Sciences

Chennai Campus

International Journal of Advanced Research in Engineering and Technology

Solving nonlinear integral equations and nonlinear integro-differential equations using laplace adomian decomposition method through sagemath

In this article an interesting procedure is proposed for fuzzy travelling salesman problems and assignment problems using " R" software packages such as "FuzzyNumbers" and "lpSolve" and fuzzy travelling salesman problems using "R" software packages "FuzzyNumbers" and "TSP". To validate the procedure some numerical examples are illustrated and the results are compared with the contemporary procedures. © 2020, Research Publication. All rights reserved.

Advances in Mathematics: Scientific Journal

Solving fuzzy assignment and fuzzy travelling salesman problems using R software

In this paper, a novel technique is proposed to solve fuzzy fractional delay differential equations (FFDDEs) with initial condition and source function, which are fuzzy triangular functions. The obtained solution is a fuzzy set of real functions. Each real function satisfies an FFDDE with a specific membership degree. A detailed algorithm is provided to solve the FFDDE. The proposed method has been elucidated in detail through numerical illustrations. Graphs are plotted using MATLAB. © 2010 2020

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Fulltext

International Journal of Fuzzy Logic and Intelligent Systems

Numerical Solutions of Fuzzy Fractional Delay Differential Equations

The Adomian decomposition method (ADM) proposed by George Adomian is one of the teachnique to solve linear as well as nonlinear differential equations that are encountered in the field of Physics, Biology and Engineering etc. Computation of Adomian Polynomials for each of the nonlinear terms is a vital activity when solving nonlinear problems using ADM method. In this paper the authors presents a SageMath program for computing Adomian polynomials through integer partition method for single variable case. The SageMath code developed in this paper is felt to be an efficient symbolic computation for generating Adomian polynomials. Also, SageMath package for solving nonlinear differential equations through Adomian decomposition method are presented in this paper. Examples of solving nonlinear ordinary, partial and fractional differential equations are given and the results confirm the applicability of the developed program. © BEIESP.

International Journal of Innovative Technology and Exploring Engineering

Solving nonlinear differential equations using adomian decomposition method through sagemath

In this article, Adomian decomposition method have been applied for getting analytical approximate solutions of time-fractional nonlinear coupled Boussinesq-Burgers equations. The solutions are compared with the exact solution at α = 1 for different values of x and t. © 2019 Author(s).

Department of Computer Applications

School of Information Technology and Engineering

Vellore Campus

AIP Conference Proceedings

Solving time-fractional nonlinear coupled Boussinesq-Burgers equations arise in propagation of shallow water waves using adomian decomposition method

Travelling Salesman Problem (TSP) is to detect the shortest closed tour such the teach city is visited exactly on ceinan n-city. The TSP problem is a special kind of an assignment model that eliminates sub-tours. In Dynamic Programming the optimum solution of a multivariable problem is obtained by decomposing sub-problem of a single variable. In this paper, Dynamic programming technique is applied to solve a Fuzzy Travelling Salesman Problem (FTSP) and MATLAB program is developed. © IAEME Publication.

International Journal of Mechanical Engineering and Technology

A new approach for solving travelling salesman problem with fuzzy numbers using dynamic programming

Department of Communication Engineering

School of Electronics Engineering

British Journal of Mathematics & Computer Science

Symbolic Computation of Adomian Polynomials Based on Rach’s Rule

In this paper, we study the unsteady boundary layer flow of an incompressible fluid over a stretching surface in the presence of a heat source or sink using Adomian decomposition method. The solutions are agreeable with the existing numerical results. © Research India Publications.

Global Journal of Pure and Applied Mathematics

A comparative study of numerical solutions and analytic solutions obtained using adomiandecomposition method for heat transfer over stretching surface with variable heat flux in the presence of a heat source or sink

Computers and Mathematics with Applications

Corrigendum to "Recursive formulation of the matrix Padé approximation in packed storage" [Comput. Math. Appl. 59 (2010) 1532-1540] (DOI:10.1016/j.camwa.2009.11.015)

The Extended Euclidean algorithm for matrix Padé approximants is applied to compute matrix Padé approximants when the coefficient matrices of the input matrix polynomial are triangular. The procedure given by Bjarne S. Anderson et al. for packing a triangular matrix in recursive packed storage is applied to pack a sequence of lower triangular matrices of a matrix polynomial in recursive packed storage. This recursive packed storage for a matrix polynomial is applied to compute matrix Padé approximants of the matrix polynomial using the Matrix Padé Extended Euclidean algorithm in packed form. The CPU time and memory comparison, in computing the matrix Padé approximants of a matrix polynomial, between the packed case and the non-packed case are described in detail. © 2009 Elsevier Ltd. All rights reserved.