A Fifth-fourth Continuous Block Implicit Hybrid Method for the Solution of Third Order Initial Value Problems in Ordinary Differential Equations
Adoghe Lawrence Osa,
Omole Ezekiel Olaoluwa
Issue:
Volume 8, Issue 3, June 2019
Pages:
50-57
Received:
30 January 2019
Accepted:
17 March 2019
Published:
12 August 2019
Abstract: In this paper, block method was developed using method of collocation and interpolation of power series as approximate solution to give a system of non linear equations which is solved to give a continuous hybrid linear multistep method. The continuous hybrid linear multistep method is solved for the independent solutions to give a continuous hybrid block method which is then evaluated at some selected grid points to give a discrete block method. The basic properties of the discrete block method were investigated and found to be zero stable, consistent and convergent. The derived scheme was tested on some numerical examples and was found to give better approximation than the existing method.
Abstract: In this paper, block method was developed using method of collocation and interpolation of power series as approximate solution to give a system of non linear equations which is solved to give a continuous hybrid linear multistep method. The continuous hybrid linear multistep method is solved for the independent solutions to give a continuous hybri...
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The Application of Bessel Function in the Definite Solution Problem of Cylindrical Coordinate System
Issue:
Volume 8, Issue 3, June 2019
Pages:
58-64
Received:
12 July 2019
Accepted:
10 August 2019
Published:
23 August 2019
Abstract: The variable separation method is an important method to solve the definite solution problems, especially the definite solution problems of cylinder and sphere regions. This method can solve these problems on cylinder and sphere regions, but the solving procedures are very difficult in the practical application. It is often solved by combining the properties of Bessel functions. In this paper, we propose a method combining Bessel function to solve homogeneous definite solution problem on the cylindrical coordinate system and give the algorithm of solving a definite problem. This algorithm is easy to implement and simplifies the process of calculation. Firstly, the definition and properties of Bessel function are briefly recalled, which are the first and essential step to solve the definite solution problem. Then we give the basic process of solving homogeneous definite solution problem, where consider the problem of the definite solution of the homogeneous wave equation, homogeneous heat conduction equation and Laplace equation. We analyze the solution of the Bessel equation definite solution problem under three kinds of boundary conditions and conclude the algorithm of solving a definite problem. At last, two numerical examples are provided to validate the feasibility of the proposed method.
Abstract: The variable separation method is an important method to solve the definite solution problems, especially the definite solution problems of cylinder and sphere regions. This method can solve these problems on cylinder and sphere regions, but the solving procedures are very difficult in the practical application. It is often solved by combining the ...
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Characteristic Vectors in p/q-Channel Orthonormal Wavelet
Zhaofeng Li,
Hongying Xiao
Issue:
Volume 8, Issue 3, June 2019
Pages:
65-69
Received:
8 July 2019
Published:
27 August 2019
Abstract: Wavelet analysis is a newly rapidly developing subject in the late twentieth century. As a time-frequency analysis tool, wavelet analysis has many advantages over other time-frequency tools, such as in signal processing, image processing, speech processing, pattern recognition, quantum physics and other fields. Multiresolution analysis (MRA for short) is an important method for studying wavelet orthonormal wavelet bases with rational dilation 2. However, p/q-band wavelet is known to have advantages over 2-band wavelet in some aspects such as in signal processing and attracted more and more interest in recent years. But there are relatively less results for the case of p/q-band. This paper studies the orthonormal wavelet bases with rational dilation factor p/q based on multiresolution analysis by a polyphase decomposition technique. First, we gave the concept of Multiresolution analysis with rational dilation p/q and deduced an identity of the masks matrix. Also, a perfect reconstruction condition in terms of masks was presented. Further, we gave the refinement and wavelet matrices respectively and derived the characteristic roots and the corresponding orthonormal characteristic vectors of the wavelet matrix, and then a method with characteristic vectors was reduced to achieve the orthonormal wavelet bases with rational dilation factor p/q. In the end, an example is offered to verify this theory.
Abstract: Wavelet analysis is a newly rapidly developing subject in the late twentieth century. As a time-frequency analysis tool, wavelet analysis has many advantages over other time-frequency tools, such as in signal processing, image processing, speech processing, pattern recognition, quantum physics and other fields. Multiresolution analysis (MRA for sho...
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