Book ChapterDOI
Linear Differential Equations
Anish Deb,Srimanti Roychoudhury,Gautam Sarkar +2 more
- pp 141-166
TLDR
In this article, the authors presented the solution of first order linear differential equations using both HF domain differentiation operational matrices and integration operational matrix, and compared the results by way of treating five examples.Abstract:
This chapter is devoted to linear differential equations . That is, it presents the solution of first order differential equations using both HF domain differentiation operational matrices and integration operational matrices. Higher order differential equations are also solved via the same first order operational matrices, and again employing one-shot integration matrices. The results are compared by way of treating five examples. Eleven figures are presented as illustration of the HF domain techniques.read more
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Book
Ordinary differential equations
TL;DR: The fourth volume in a series of volumes devoted to self-contained and up-to-date surveys in the theory of ODEs was published by as discussed by the authors, with an additional effort to achieve readability for mathematicians and scientists from other related fields so that the chapters have been made accessible to a wider audience.
Journal ArticleDOI
Numerical methods for ordinary differential equations in the 20th century
TL;DR: This survey paper follows the main strands in the developments of these methods, both for general problems, stiff systems, and for many of the special problem types that have been gaining in significance as the century draws to an end.
Book
Piecewise Constant Orthogonal Functions and Their Application to Systems and Control
TL;DR: In this article, the authors proposed piecewise constant orthogonal basis functions (PCF) for linear and non-linear linear systems, and the optimal control of linear lag-free and time-lag systems.
Journal ArticleDOI
A Sequence of Piecewise Orthogonal Polynomials
Y. Y. Feng,D. X. Qi +1 more
TL;DR: In this article, the construction of an orthogonal sequence of piecewise polynomials of degree k which is complete in time O(L_2 ) is studied.