Solution of some parabolic inverse problems by homotopy analysis method

Numerical Solution of Fuzzy Linear Volterra Integral Equations of the Second Kind by Homotopy Analysis Method

solution of security constrained unit commitment problem by a new multi-objective optimization method

چکیده-پخش بار بهینه به عنوان یکی از ابزار زیر بنایی برای تحلیل سیستم های قدرت پیچیده ،برای مدت طولانی مورد بررسی قرار گرفته است.پخش بار بهینه توابع هدف یک سیستم قدرت از جمله تابع هزینه سوخت ،آلودگی ،تلفات را بهینه می کند،و هم زمان قیود سیستم قدرت را نیز برآورده می کند.در کلی ترین حالتopf یک مساله بهینه سازی غیر خطی ،غیر محدب،مقیاس بزرگ،و ایستا می باشد که می تواند شامل متغیرهای کنترلی پیوسته و گ...

A homotopy method for nonlinear inverse problems q

We develop a homotopy method for nonlinear inverse problems, where the forward problems are governed by some forms of differential equations. A Tikhonov-style regularization approach yields an optimization problem. Ordinary iterative methods may fail to solve this problem, due to their locally convergent properties. Then the fixed-point homotopy method is introduced to solving the normal equati...

Solving a System of Linear Equations by Homotopy Analysis Method

‎In this paper‎, ‎an efficient algorithm for solving a system of linear‎ ‎equations based on the homotopy analysis method is presented‎. ‎The‎ ‎proposed method is compared with the classical Jacobi iterative‎ ‎method‎, ‎and the convergence analysis is discussed‎. ‎Finally‎, ‎two‎ ‎numerical examples are presented to show the effectiveness of the‎ ‎proposed method.‎

Inverse problems for parabolic equations

Let ut −∇2u = f(x) := ∑M m=1 amδ(x− xm) in D × [0,∞), where D ⊂ R3 is a bounded domain with a smooth connected boundary S, am = const, δ(x− xm) is the delta-function. Assume that u(x, 0) = 0, u = 0 on S. Given the extra data u(yk, t) := bk(t), 1 ≤ k ≤ K, can one find M,am, and xm? Here K is some number. An answer to this question and a method for finding M,am, and xm are given.