Journal•ISSN: 1312-7586
The International Journal of Contemporary Mathematical Sciences
Hikari, Ltd.
About: The International Journal of Contemporary Mathematical Sciences is an academic journal published by Hikari, Ltd.. The journal publishes majorly in the area(s): Mathematics Subject Classification & Space (mathematics). It has an ISSN identifier of 1312-7586. Over the lifetime, 601 publications have been published receiving 2054 citations.
Topics: Mathematics Subject Classification, Space (mathematics), Nonlinear system, Fibonacci number, Fuzzy logic
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TL;DR: In this article, the convergence of q-homotopy analysis method (q-HAM) is studied and it is proven that under certain conditions the solution of the equation is known.
Abstract: The convergence of q- homotopy analysis method (q-HAM) is studied in the present paper. It is proven that under certain conditions the solution of the equation:
78 citations
TL;DR: In this article, the application of differential transformation method (DTM) to solve the Bratu problem is presented. And two special cases of the problem are illustrated by using the technique and numerical results and conclusions.
Abstract: This paper is the application of differential transformation method (DTM) to solve the Bratu problem. A considerable research works have been conducted recently in applying DTM to different types of partial differential equation of Abdel-Halim Hassan (Chaos, Solitons & Fractals [6]) and fractional differential equations of Arikoglu and Ozkol (Chaos, Solitons & Fractals [1]). The nonlinear eigenvalue problem 0 = + Δ u e u λ in the unit square with u = 0 on the boundary 1494 I. H. Abdel-Halim Hassan and Vedat Suat Erturk is often referred to as "the Bratu problem". The Bratu problem in one-dimensional planar coordinates 0 = + ′ ′ u e u λ with u(0) = u(1) = 0 has two known, bifurcated solutions for values of c λ λ and a unique solution when c λ λ = . The value of c λ is related to the fixed point of hyperbolic cotangent function. Two special cases of the problem are illustrated by using the technique and numerical results and conclusions will be presented. Mathematics Subject Classification: 74S30, 34B15
71 citations
TL;DR: In this article, a new algorithm for calculating Adomian polynomials for nonlinear functional functions with several variables is presented, which requires less computations in comparison with the previous methods.
Abstract: In this paper, we introduce a new Algorithm for calculating Adomian polynomials and present some example to show the simplicity of the new Algorithm. The new Algorithm requires less computations in comparison with the previous methods, and can be extended to calculate Adomian polynomials for nonlinear functional with several variables.
49 citations
TL;DR: For the case k = 2, the Bertrand's postulate was proved for the first time by P. L. Chebyshev in 1850, and simplified later by Erdős in 1932.
Abstract: Is it true that for all integer n > 1 and k ≤ n there exists a prime number in the interval [kn, (k + 1)n]? The case k = 1 is the Bertrand’s postulate which was proved for the first time by P. L. Chebyshev in 1850, and simplified later by P. Erdős in 1932, see [2]. The present paper deals with the case k = 2. A positive answer to the problem for any k ≤ n implies a positive answer to the old problem whether there is always a prime in the interval [n, n + n], see [1, p. 11].
44 citations
40 citations