Open Access Original Research Article

The Solitary Travelling Wave Solutions of Some Nonlinear Partial Differential Equations Using the Modified Extended Tanh Function Method with Riccati Equation

M. M. El-Horbaty, F. M. Ahmed

Asian Research Journal of Mathematics, Page 1-13
DOI: 10.9734/ARJOM/2018/36887

In this work, we aimed to construct a variety of solitary travelling wave solutions of a wide class of nonlinear partial differential equations (PDE's) that is governed by a presented single nonlinear partial differential equation (PDE) using the powerful modified extended Tanh method with Riccati equation. More general solutions are successfully constructed including the previous known formal solutions such as shock wave, periodic and weirstrass solutions.

Open Access Original Research Article

Open Access Original Research Article

Approximate Analytical Solution of Index-2 DAEs Arising from Constrained Multibody Systems

Brahim Benhammouda

Asian Research Journal of Mathematics, Page 1-15
DOI: 10.9734/ARJOM/2018/38983

Constrained multibody mechanical systems are used in various applications. These systems often lead to index-2 or index-3 differential-algebraic equations (DAEs), which are known to pose a challenge to numerical integration methods. This paper develops a novel approach to solve index- 2 DAEs which describe the dynamics of constrained multibody mechanical systems. The method, called PSMAP, relies on effective combination of the power series method (PSM) with Adomian polynomials (AP). To overcome the limitation of the PSM, the PSMAP expands nonlinear terms once in series form using AP. Further, by exploiting an important property of AP, a nonsingular linear algebraic system for the coefficients of the power series solution is derived and solved. To extend the domain of the power series solution, a multistage PSMAP is developed. The main advantage of our technique is that it applies directly to the DAE without the need for complex or costly transformations like index-reductions. Consequently, the PSMAP considerably reduces the computation work, leads to simple algorithm and avoids constraints violation. To demonstrate the efficiency of the PSMAP, two examples of two-link planar robotic systems are solved. Numerical results show that the PSMAP is a powerful tool to solve this class of DAEs.

Open Access Original Research Article

Comparison of Jacobi and Gauss-Seidel Iterative Methods for the Solution of Systems of Linear Equations

A. I. Bakari, I. A. Dahiru

Asian Research Journal of Mathematics, Page 1-7
DOI: 10.9734/ARJOM/2018/34769

In this research work two iterative methods of solving system of linear equation has been compared, the iterative methods are used for solving sparse and dense system of linear equation and the methods were being considered are: Jacobi method and Gauss-Seidel method. The results show that Gauss-Seidel method is more efficient than Jacobi method by considering maximum number of iteration required to converge and accuracy.

Open Access Original Research Article

Some Geometric Properties of a Generalized Difference Sequence Space Involving Lacunary Sequence

Sushomita Mohanta

Asian Research Journal of Mathematics, Page 1-13
DOI: 10.9734/ARJOM/2018/39783

In this paper, we define a new generalized difference sequence space l(p, θ,Δm, s) involving lacunary sequence where p = (pr) is a bounded sequence of positive real numbers with pr > 1 for all r ∈ and s ≥ 0. Then, we examine the uniform Opial property, k-NUC property and Banach-Saks property of type p for this space.