International Journal of Modern Mathematical Sciences
ISSN: 2166-286X (online)Search Article(s) by:
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Current Issue: Vol. 19 No. 2or Keyword in Title:
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Table of Content for Vol. 19 No. 2, 2021

Wavelet Preconditioned Method for the Numerical Solution of Stochastic Differential Equations
Mounesha H. Kantli, Manjunathayya M. Holliyavar
      
 PP. 90 - 99
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ABSTRACT: In this paper, wavelet preconditioned method is used for the numerical solution of stochastic differential equation. The proposed method is the robust technique for faster convergence with low computational cost which is acceptable through error ( ) and CPU time. It is concluded that the wavelet preconditioned technique easily outperforms over existing standard classical preconditioned methods.


Matrix, Group, Tensor and Corresponding Mathematical Quantum Theory and Its Applications
Yi-Fang Chang
      
 PP. 100 - 115
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ABSTRACT: Based on the non-commutation [A,B]=AB-BA=η≠0 of matrix, group, tensor and so on, we propose the mathematical quantum theory. If is imaginary number, it will correspond to the extensive quantum theory. If η is real number, it will be development of quantum theory. Moreover, η  may be complex number, etc. We introduce a similar wave function and corresponding operators, various similar quantum results will be derived. Next, we discuss its physical meaning and various applications. Third, based the general matrix we research mathematics of unified gravitational and electromagnetic fields. Fourth, we discuss the space-time equations and the simplest unifying quantum theory and general relativity. Further, we can combine general discrete mathematics.


Numerical Solution of Singular Boundary Value Problems Using Boubaker Wavelet Based Galerkin Method
L. M. Angadi
      
 PP. 116 - 125
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ABSTRACT: In this paper, we proposed the numerical solution of Singular boundary value problems (SBVPs) using Boubaker wavelet based Galerkin method (BWGM). Here, Boubaker wavelets are used as weight functions and these are assumed bases elements which allow us to obtain the numerical solutions of the singular boundary value problems. The obtained numerical results using this method are compared with the exact solution and existing methods (FDM, LWGM, HWGM). Some of the problems are taken to demonstrate the applicability and validity of the proposed method.