Taylor-newton homotopy method for computing the depth of flow rate for a channel

Homotopy approximation methods (HAM) can be considered as one of the new methods belong to the general classification of the computational methods which can be used to find the numerical solution of many types of the problems in science and engineering. The general problem relates to the flow and the depth of water in open channels such as rivers and canals is a nonlinear algebraic equation which is known as continuity equation. The solution of this equation is the depth of the water. This paper represents attempt to solve the equation of depth and flow using Newton homotopy based on Taylor series. Numerical example is given to show the effectiveness of the purposed method using MATLAB language

ニュートン不動点ホモトピーを用いた非線形回路の直流動作点の大域的求解法

In circuit simulation, many circuit designers experience difficulties in finding dc operating points of nonlinear circuits because the Newton-Raphson method often fails to converge unless the initial point is sufficiently close to the solution. To overcome this convergence problem, homotopy methods have been studied, and it has been proved that the homotopy methods are globally convergent for nonlinear circuit equations. Nowadays the homotopy methods are widely used in practical circuit simulation, and bipolar analogin tegrated circuits with more than 20,000 elements are solved efficiently with the theoretical guarantee of global convergence. In this paper, an efficient algorithm using a new homotopy function termed the Newton-fixed-point homotopy is proposed, and it is shown that this algorithm is more efficient than the conventional algorithms.【査読有