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Finite Difference Schemes for Differential Equations [PDF]

Mathematics of Computation, 1964
(1) ~~~~~L = d p(x) d + q(x) and the related variational problem for the functional b ~~~~~~~~~~b (2) Q(u) = ] (pu'2 + qu') dx - 2 fu dx viz., min Q(u) uE Q where the class Q consists of smooth functions u(x) satisfying u(a) = u(b) = 0. Following Ritz, the solution of the variational problem may be discussed within the framework of the direct methods ...
openaire   +2 more sources

A Robust Adaptive One‐Sample‐Ahead Preview Super‐Twisting Sliding Mode Controller

International Journal of Adaptive Control and Signal Processing, EarlyView.
Block Diagram of the Robust Adaptive One‐Sample‐Ahead Preview Super‐Twisting Sliding Mode Controller. ABSTRACT This article introduces a discrete‐time robust adaptive one‐sample‐ahead preview super‐twisting sliding mode controller. A stability analysis of the controller by Lyapunov criteria is developed to demonstrate its robustness in handling both ...
Guilherme Vieira Hollweg, Paulo Jefferson Dias de Oliveira Evald, Shivam Chaturvedi, Hilton Abilio Gründling, Rodrigo Varella Tambara, Wencong Su   +5 more
wiley   +1 more source

Exact Finite-Difference Schemes for d-Dimensional Linear Stochastic Systems with Constant Coefficients

Journal of Applied Mathematics, 2013
The authors attempt to construct the exact finite-difference schemes for linear stochastic differential equations with constant coefficients. The explicit solutions to Itô and Stratonovich linear stochastic differential equations with constant ...
Peng Jiang, Xiaofeng Ju, Dan Liu, Shaoqun Fan   +3 more
doaj   +1 more source

Construction of Compact Finite Difference Schemes by Classic Differential Quadrature

Applied Sciences, 2017
Using classic differential quadrature formulae and uniform grids, this paper systematically constructs a variety of high-order finite difference schemes, and some of these schemes are consistent with the so-called boundary value methods.
Fangzong Wang, Mingshuai Pan, Yong Wang
doaj   +1 more source

High-order conservative finite difference GLM-MHD schemes for cell-centered MHD [PDF]

, 2010
We present and compare third- as well as fifth-order accurate finite difference schemes for the numerical solution of the compressible ideal MHD equations in multiple spatial dimensions.
Bodo, G., Mignone, A., Tzeferacos, P.
core   +2 more sources

Thermoreflectance Detection of Point Defects Resulting from Focused Ion Beam Milling

Advanced Engineering Materials, EarlyView.
Focused ion beam (FIB) milling is a common tool for nanoscale material processing, however irradiation damage, redeposition, and contamination can occur. We use several characterization tools to show FIB‐induced effects beyond 1 mm from the milled area.
Thomas W. Pfeifer, Eric R. Hoglund, Anton V. Ievlev, Patrick E. Hopkins   +3 more
wiley   +1 more source

High-Order, Accurate Finite Difference Schemes for Fourth-Order Differential Equations

Axioms
This article is devoted to the study of high-order, accurate difference schemes’ numerical solutions of local and non-local problems for ordinary differential equations of the fourth order. Local and non-local problems for ordinary differential equations
Allaberen Ashyralyev, Ibrahim Mohammed Ibrahım   +1 more
doaj   +1 more source

Two Conservative Difference Schemes for Rosenau-Kawahara Equation

Advances in Mathematical Physics, 2014
Two conservative finite difference schemes for the numerical solution of the initialboundary value problem of Rosenau-Kawahara equation are proposed. The difference schemes simulate two conservative quantities of the problem well.
Jinsong Hu, Youcai Xu, Bing Hu, Xiaoping Xie   +3 more
doaj   +1 more source

Characterization of Defect Distribution in an Additively Manufactured AlSi10Mg as a Function of Processing Parameters and Correlations with Extreme Value Statistics

Advanced Engineering Materials, EarlyView.
Predicting extreme defects in additive manufacturing remains a key challenge limiting its structural reliability. This study proposes a statistical framework that integrates Extreme Value Theory with advanced process indicators to explore defect–process relationships and improve the estimation of critical defect sizes. The approach provides a basis for
Muhammad Muteeb Butt, Varma Kvvssn, Hossein Laieghi, Zia Uddin, Peyman Ansari, E. Kıvanç Sadak, Can Barış Toprak, Hüseyin Kızıl, Enrico Salvati   +8 more
wiley   +1 more source

Stability of central finite difference schemes for the Heston PDE

, 2010
This paper deals with stability in the numerical solution of the prominent Heston partial differential equation from mathematical finance. We study the well-known central second-order finite difference discretization, which leads to large semi-discrete ...
A Böttcher, A Lipton, D Tavella, E Hairer, E Hairer, JC Butcher, K Volders, Karel J. in ’t Hout, Kim Volders, KJ in ’t Hout, LN Trefethen, P Wilmott, SE Shreve, SL Heston, W Hundsdorfer   +14 more
core   +1 more source