Results 21 to 30 of about 892,367 (145)

A new high accurate approximate approach to solve optimal control problems of fractional order via efficient basis functions

Alexandria Engineering Journal, 2022
Investigation of spectral (collocation or Galerkin) methods for the solution approximation of different classes of optimal control problems have had been increased in recent years.
Pang Xiaobing, Xingfa Yang, Mohammad Hadi Noori Skandari, Emran Tohidi, Stanford Shateyi   +4 more
doaj   +1 more source

New recursive approximations for variable-order fractional operators with applications

Mathematical Modelling and Analysis, 2018
To broaden the range of applicability of variable-order fractional differential models, reliable numerical approaches are needed to solve the model equation.In this paper, we develop Laguerre spectral collocation methods for solving variable-order ...
Mahmoud A. Zaky, Eid H. Doha, Taha M. Taha, Dumitru Baleanu   +3 more
doaj   +1 more source

Numerical solution of time-dependent Emden-Fowler equations using bivariate spectral collocation method on overlapping grids

Nonlinear Engineering, 2020
In this work, we present a new modification to the bivariate spectral collocation method in solving Emden-Fowler equations. The novelty of the modified approach is the use of overlapping grids when applying the Chebyshev spectral collocation method.
Mkhatshwa Musawenkhosi P., Motsa Sandile S., Sibanda Precious   +2 more
doaj   +1 more source

Chebyshev collocation method for solving second order ODEs using integration matrices

Discrete and Continuous Models and Applied Computational Science, 2023
The spectral collocation method for solving two-point boundary value problems for second order differential equations is implemented, based on representing the solution as an expansion in Chebyshev polynomials. The approach allows a stable calculation of
Konstantin P. Lovetskiy, Dmitry S. Kulyabov, Leonid A. Sevastianov, Stepan V. Sergeev   +3 more
doaj   +1 more source

Numerical investigations of a new singular second-order nonlinear coupled functional Lane–Emden model

Open Physics, 2020
The present study aims to design a second-order nonlinear Lane–Emden coupled functional differential model and numerically investigate by using the famous spectral collocation method.
Abdelkawy Mohamed A., Sabir Zulqurnain, Guirao Juan L. G., Saeed Tareq   +3 more
doaj   +1 more source

A High-Efficiency Spectral Method for Two-Dimensional Ocean Acoustic Propagation Calculations

Entropy, 2021
The accuracy and efficiency of sound field calculations highly concern issues of hydroacoustics. Recently, one-dimensional spectral methods have shown high-precision characteristics when solving the sound field but can solve only simplified models of ...
Xian Ma, Yongxian Wang, Xiaoqian Zhu, Wei Liu, Wenbin Xiao, Qiang Lan   +5 more
doaj   +1 more source

On the bivariate spectral quasi-linearization method for solving the two-dimensional Bratu problem

Open Physics, 2018
In this paper, a bivariate spectral quasi-linearization method is used to solve the highly non-linear two dimensional Bratu problem. The two dimensional Bratu problem is also solved using the Chebyshev spectral collocation method which uses Kronecker ...
Muzara Hillary, Shateyi Stanford, Tendayi Marewo Gerald   +2 more
doaj   +1 more source

Collocation schemes for periodic solutions of neutral delay differential equations [PDF]

, 2005
We introduce two collocation schemes for the computation of periodic solutions of neutral delay differential equations (NDDEs): one based on a direct discretisation of the underlying NDDE, and one based on a discretisation of a related delay differential
Wilson, RE, Krauskopf, B., Wilson, R. Eddie, Wilson, R.E., Barton, DAW, Barton, D.A.W., Barton, David A.W., Krauskopf, B, Krauskopf, Bernd   +8 more
core   +1 more source

Space-Time Spectral Collocation Algorithm for the Variable-Order Galilei Invariant Advection Diffusion Equations with a Nonlinear Source Term

Mathematical Modelling and Analysis, 2017
This paper presents a space-time spectral collocation technique for solving the variable-order Galilei invariant advection diffusion equation with a nonlinear source term (VO-NGIADE).
Mohamed A. Abd-Elkawy, Rubayyi T. Alqahtani   +1 more
doaj   +1 more source

Numerical approximation of space-fractional diffusion equation using Laguerre spectral collocation method

International Journal of Mathematics for Industry
The space-fractional diffusion equation is extensively used to model various issues in engineering and mathematics. This paper addresses the numerical approximation of the space-fractional-order diffusion equation, using a fractional operator in the ...
Minilik Ayalew, Mekash Ayalew, Mulualem Aychluh   +2 more
doaj   +1 more source