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Differential transform method: A comprehensive review and analysis [PDF]
Iranian Journal of Numerical Analysis and Optimization, 2022 The complexity of solving differential equations in real-world applications motivates researchers to extend numerical methods. Among different numerical and semi-analytical methods for solving initial and boundary value problems, the differential ...
S.H. Hashemi Mehne
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Different Groups of Variational Principles for Whitham-Broer-Kaup Equations in Shallow Water [PDF]
Journal of Applied and Computational Mechanics, 2020 Because the variational theory is the theoretical basis for many kinds of analytical or numerical methods, it is an essential but difficult task to seek explicit functional formulations whose extrema are sought by the nonlinear and complex models. By the
Xiao-Qun Cao +4 more
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Flow development region in the boundary layer: two-component molecular viscosity and partial slip
Авіаційно-космічна техніка та технологія, 2023 The subject of this study is the flow development region of laminar incompressible fluid flow in the boundary layer. This flow is an example where a direct application of the Navier-Stokes equations of gradient-free laminar incompressible fluid flow, in ...
Pavlo Lukianov, Lin Song
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Numerical solution of fractional Sturm-Liouville equation in integral form [PDF]
, 2014 In this paper a fractional differential equation of the Euler-Lagrange / Sturm-Liouville type is considered. The fractional equation with derivatives of order $\alpha \in \left( 0,1 \right]$ in the finite time interval is transformed to the integral form.
Blaszczyk, Tomasz, Ciesielski, Mariusz
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Regge Calculus as a Fourth Order Method in Numerical Relativity [PDF]
, 1995 The convergence properties of numerical Regge calculus as an approximation to continuum vacuum General Relativity is studied, both analytically and numerically.
Barrett J W +15 more
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Chaos Theory and Applications, 2022 Complex problems in nonlinear dynamics foreground the critical support of artificial phenomena so that each domain of complex systems can generate applicable answers and solutions to the pressing challenges.
Dumitru Baleanu, Yeliz Karaca
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Discrete mechanics and optimal control: An analysis [PDF]
, 2009 The optimal control of a mechanical system is of crucial importance in many application areas. Typical examples are the determination of a time-minimal path in vehicle dynamics, a minimal energy trajectory in space mission design, or optimal motion ...
Junge, Oliver +2 more
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Recent Progress in Regge Calculus [PDF]
, 1997 While there has been some advance in the use of Regge calculus as a tool in numerical relativity, the main progress in Regge calculus recently has been in quantum gravity. After a brief discussion of this progress, attention is focussed on two particular,
Ambjorn +19 more
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A survey on fractional variational calculus
, 2018 Main results and techniques of the fractional calculus of variations are surveyed. We consider variational problems containing Caputo derivatives and study them using both indirect and direct methods.
Almeida, Ricardo, Torres, Delfim F. M.
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A Total Fractional-Order Variation Model for Image Restoration with Non-homogeneous Boundary Conditions and its Numerical Solution [PDF]
, 2015 To overcome the weakness of a total variation based model for image restoration, various high order (typically second order) regularization models have been proposed and studied recently.
Chen, Ke, Zhang, Jianping
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