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Frontiers

Editorial: Approximation methods and analytical modeling using partial differential equations

Adequate mathematical modeling is the key to success for many real-world projects in engineering, medicine, and other applied areas. Once a well-suited model is established, it can be thoroughly ...
Nature

i. Elements of the Differential Calculus, with Examples and Applications: a Text-book. ii. An Elementary Treatise on the Differential Calculus, founded on the Method of Rates ...

NEARLY five years have passed since we noticed a small pamphlet by the authors of (ii.), together with treatises on the calculus of Messrs. Buckingham (Chicago) and Clark (Cincinnati), and we then ...
JSTOR Daily

A High-Order Difference Method for Differential Equations

This paper analyzes a high-accuracy approximation to the $m$th-order linear ordinary differential equation $Mu = f$. At mesh points, $U$ is the estimate of $u$; and ...
IEEE

On the Numerical Approximation of First-order Riccati Differential Equations by Two-step Second Derivative Block Method with Bernstein Polynomial Basis

Abstract: A new two-step second derivative block method (TSDBM) using Bernstein polynomial of convergence order six for solving Riccati Differential Equations (RDEs) is presented. The TSDBM is ...
IEEE

A Progressive Polyhedral Approximation Method for Nonlinear PDE-Constrained Electricity-Water Nexus Dispatch

Abstract: This letter proposes an efficient progressive polyhedral approximation (PA) method to tackle the high nonlinearity and nonconvexity of optimal electricity-water nexus (EWN) dispatch caused ...
JSTOR Daily

AN ANISOTROPIC SPARSE GRID STOCHASTIC COLLOCATION METHOD FOR PARTIAL DIFFERENTIAL EQUATIONS WITH RANDOM INPUT DATA

SIAM Journal on Numerical Analysis, Vol. 46, No. 5 (2008), pp. 2411-2442 (32 pages) This work proposes and analyzes an anisotropic sparse grid stochastic collocation method for solving partial ...