摘要:

The utility of piecewise-linear polynomial functions for solving stiff equations is investigated. Based on the concept of the operational matrix, the stiff systems are reduced to an algebraic recurrence form. Examples are given to demonstrate the usefulness of this method for both linear and non-linear stiff systems. The results are satisfactory.

ISSN:0020-7721    

DOI:10.1080/00207728708967191

出版商:Taylor & Francis Group    

年代:1987

数据来源: Taylor

摘要:

By using the expansions of piecewise-linear polynomial functions, the Sturm-Liouville eigenvalue problem can be dealt with as a set of linear algebraic equations. Owing to the available recursive algorithm, these linear algebraic equations can be solved by straightforward substitution. An iterative improvement is used for finding eigenvalues in order to speed up the convergence. The usefulness of this method is demonstrated by an example and the results are satisfactory.

ISSN:0020-7721    

DOI:10.1080/00207728708967192

出版商:Taylor & Francis Group    

年代:1987

数据来源: Taylor

摘要:

Generalized orthogonal polynomials which include all types of orthogonal polynomial are introduced first. Using the idea of orthogonal polynomials that can be expressed by a Taylor power series and vice versa, the operational matrix for the integration of the generalized orthogonal polynomials is first derived. A stretched operational matrix of diagonal form is also derived. Both the operational matrix for the integration and the stretched operational matrix of generalized orthogonal polynomials are applied to solve functional differential equations. The characteristics of each kind of orthogonal polynomial in solving the scaled system is demonstrated. The computational strategy for finding the expansion coefficients of the state variables is very simple, straightforward and easy. The inversion of only one matrix, which has the same dimension as the state variables, is required. The expansion coefficients of the state variables are obtained by the proposed recursive formula. Much computer time is thus saved and computational results are obtained that are very accurate compared with previous methods.

ISSN:0020-7721    

DOI:10.1080/00207728708967193

出版商:Taylor & Francis Group    

年代:1987

数据来源: Taylor

摘要:

The scaled Taylor operational and transformation matrices of polynomial series are introduced for analysing and approximating the solution of the functional differential equation of a scaled system with a constant scale. The parameter identification problem of the scaled system is also tackled. Illustrative examples with satisfactory results are given. The results are in accordance with exact solutions.

ISSN:0020-7721    

DOI:10.1080/00207728708967194

出版商:Taylor & Francis Group    

年代:1987

数据来源: Taylor

摘要:

The Fourier exponential operational matrix of integrationPis derived which is analogous to that previously derived for other types of orthogonal functions. This matrixPmay be used to solve problems such as identification, analysis and optimal control.

ISSN:0020-7721    

DOI:10.1080/00207728708967195

出版商:Taylor & Francis Group    

年代:1987

数据来源: Taylor