Browsing by Author "Singh, Harendra"

Now showing 1 - 4 of 4

Citation - WoS: 19
Citation - Scopus: 51
Computational Study of Fractional Order Smoking Model
(Pergamon-elsevier Science Ltd, 2021) Baleanu, Dumitru; Singh, Jagdev; Dutta, Hemen; Singh, Harendra; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
Smoking is a very challenging problem the world is facing every day. It contributes to deaths and major health problems to millions of people every year around the world. A lot of work has been devoted to study how to minimize smoking in the society. Here we study non-integer order smoking model using an iterative scheme which is combination of discretization of domain and short memory principle. We will also discuss stability of the proposed model and used iterative scheme. CPU time is listed in tabular to show the efficiency and figures are used to show behaviour of solution in long time. The proposed technique has high accuracy and low computational cost. Using figures fractional time behaviour of solution is also plotted. (C) 2020 Published by Elsevier Ltd.
An Efficient Algorithm for the Numerical Evaluation of Pseudo Differential Operator With Error Estimation
(Amer inst Mathematical Sciences-aims, 2022) Pandey, Amit K.; Tripathi, Manoj P.; Singh, Harendra; Rao, Pentyala S.; Kumar, Devendra; Baleanu, D.; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
In this paper we introduce an efficient and new numerical algorithm for evaluating a pseudo differential operator. The proposed algorithm is time saving and fruitful. The theoretical as well as numerical error estimation of the algorithm is established, together with its stability analysis. We have provided numerical illustrations and established that the numerical findings echo the analytical findings. The proposed technique has a convergence rate of order three. CPU time of computation is also listed. Trueness of numerical findings are validated using figures.
Citation - WoS: 11
Citation - Scopus: 16
Solution of Multi-Dimensional Fredholm Equations Using Legendre Scaling Functions
(Elsevier, 2020) Baleanu, D.; Srivastava, H. M.; Dutta, Hemen; Jha, Navin Kumar; Singh, Harendra; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
In this article, we construct approximate solution to multi-dimensional Fredholm integral equations of second kind using n-dimensional Legendre scaling functions. Error analysis of the problem is provided in the L-2 sense. It is shown that our numerical method is numerically stable. Some examples are discussed based on proposed method to show the importance and accuracy of the proposed numerical method. (C) 2019 IMACS. Published by Elsevier B.V. All rights reserved.
Citation - WoS: 22
Citation - Scopus: 25
Stable Numerical Approach for Fractional Delay Differential Equations
(Springer Wien, 2017) Pandey, Rajesh K.; Baleanu, D.; Singh, Harendra; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
In this paper, we present a new stable numerical approach based on the operational matrix of integration of Jacobi polynomials for solving fractional delay differential equations (FDDEs). The operational matrix approach converts the FDDE into a system of linear equations, and hence the numerical solution is obtained by solving the linear system. The error analysis of the proposed method is also established. Further, a comparative study of the approximate solutions is provided for the test examples of the FDDE by varying the values of the parameters in the Jacobi polynomials. As in special case, the Jacobi polynomials reduce to the well-known polynomials such as (1) Legendre polynomial, (2) Chebyshev polynomial of second kind, (3) Chebyshev polynomial of third and (4) Chebyshev polynomial of fourth kind respectively. Maximum absolute error and root mean square error are calculated for the illustrated examples and presented in form of tables for the comparison purpose. Numerical stability of the presented method with respect to all four kind of polynomials are discussed. Further, the obtained numerical results are compared with some known methods from the literature and it is observed that obtained results from the proposed method is better than these methods.