Current Issue : January - March Volume : 2020 Issue Number : 1 Articles : 5 Articles
This paper aims to present, in a unified manner, algebraic techniques for linear\nequations which are valid on both the algebras of quaternions and split\nquaternions. This paper, introduces a concept of v-quaternion, studies the\nproblem of v-quaternionic linear equations by means of a complex representation\nand a real representation of v-quaternion matrices, and gives two algebraic\nmethods for solving v-quaternionic linear equations. This paper also\ngives a unification of algebraic techniques for quaternionic and split quaternionic\nlinear equations in quaternionic and split quaternionic mechanics....
In this paper, extended homogeneous balance method is presented with the aid of computer\nalgebraic system Mathematica for deriving new exact traveling wave solutions for the foam drainage\nequation and the Kowerteg-de Vriesâ??Burgers equation which have many applications in industrial\napplications and plasma physics. The method is effective to construct a series of analytical solutions\nincluding many types like periodical, rational, singular, shock, and soliton wave solutions for a wide\nclass of nonlinear evolution equations in mathematical physics and engineering sciences....
In this note we consider some basic, yet unusual, issues pertaining to the accuracy\nand stability of numerical integration methods to follow the solution\nof first order and second order initial value problems (IVP). Included are remarks\non multiple solutions, multi-step methods, effect of initial value perturbations,\nas well as slowing and advancing the computed motion in second\norder problems....
In this paper, two new refinements of the Erdösâ??Mordell inequality and three new\nrefinements of Barrowâ??s inequality are established. Some related interesting conjectures are\nput forward....
A new numerical method for tackling the three-dimensional Hestonâ??Hullâ??White partial\ndifferential equation (PDE) is proposed. This PDE has an application in pricing options when not\nonly the asset price and the volatility but also the risk-free rate of interest are coming from stochastic\nnature. To solve this time-dependent three-dimensional PDE as efficiently as possible, high order\nadaptive finite difference (FD) methods are applied for the application of method of lines. It is derived\nthat the new estimates have fourth order of convergence on non-uniform grids. In addition, it is\nproved that the overall procedure is conditionally time-stable. The results are upheld via several\nnumerical tests....
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