Journal ArticleDOI
A new set of orthogonal functions and its application to the analysis of dynamic systems
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It has been established with illustration that the TF domain technique is more accurate than the BPF domain technique as far as integration is concerned, and it provides with a piecewise linear solution.Abstract:
The present work proposes a complementary pair of orthogonal triangular function (TF) sets derived from the well-known block pulse function (BPF) set. The operational matrices for integration in TF domain have been computed and their relation with the BPF domain integral operational matrix is shown. It has been established with illustration that the TF domain technique is more accurate than the BPF domain technique as far as integration is concerned, and it provides with a piecewise linear solution. As a further study, the newly proposed sets have been applied to the analysis of dynamic systems to prove the fact that it introduces less mean integral squared error (MISE) than the staircase solution obtained from BPF domain analysis, without any extra computational burden. Finally, a detailed study of the representational error has been made to estimate the upper bound of the MISE for the TF approximation of a function f ( t ) of Lebesgue measure.read more
Citations
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Numerical solution of nonlinear Volterra-Fredholm integral equations by using new basis functions
Mahmoud Paripour,Mahdi Kamyar +1 more
TL;DR: In this article, a numerical method to solve the nonlinear Volterra-Fredholm integral equations by new basis functions (NFs) was presented by using a complementary pair of new orthogonal basis functions set derived from the well-known block pulse functions set.
Journal ArticleDOI
Solution of nonlinear fractional diffusion-wave equation by traingular functions
TL;DR: In this paper, a new technique for solving fractional diffusion-wave equation is proposed based on Triangular Function (TFs) methods, a new fractional operational matrix of integration for the TFs is derived.
Journal ArticleDOI
National economies in state-space of fractional-order financial system
TL;DR: In this article, the authors presented a method for solving national economies in state space with fractional order, where the triangular function operational matrix of the fractional-order integration was used to solve the national economies equation.
Journal ArticleDOI
Triangular functions for numerical solution of the nonlinear Volterra integral equations
TL;DR: In this paper, a new numerical iterative method based on the successive approximations method for solving nonlinear Hammerstein Volterra integral equations of the second kind is proposed.
Journal ArticleDOI
Three-dimensional triangular functions and their applications for solving nonlinear mixed Volterra–Fredholm integral equations
Farshid Mirzaee,Elham Hadadiyan +1 more
TL;DR: In this article, the authors used the 3D triangular functions (3D-TFs) for numerical solution of three-dimensional nonlinear mixed Volterra-Fredholm integral equations.
References
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Zur Theorie der orthogonalen Funktionensysteme
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G.P. Rao,Heinz Unbehauen +1 more
TL;DR: Continuous-time model-based system identification as mentioned in this paper is a well-established field in the field of control systems and is concerned with the determination of particular models for systems that are intended for a certain purpose such as control.
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Walsh operational matrices for fractional calculus and their application to distributed systems
C.F. Cheng,Y.T. Tsay,Tao Wu +2 more
TL;DR: In this paper, the Walsh operational matrix for performing integration and solving state equations is generalized to fractional calculus for investigating distributed systems and a new set of orthogonal functions is derived from Walsh functions.