By Xu Y., Bao W.

**Read Online or Download A 1/3 Pure Subharmonic Solution and Transient Process for the Duffings Equation PDF**

**Similar mathematics books**

**Mathematical Problems and Proofs: Combinatorics, Number Theory, and Geometry**

A steady advent to the hugely refined international of discrete arithmetic, Mathematical difficulties and Proofs offers subject matters starting from simple definitions and theorems to complicated themes -- comparable to cardinal numbers, producing capabilities, houses of Fibonacci numbers, and Euclidean set of rules.

**Graphs, matrices, and designs: Festschrift in honor of Norman J. Pullman**

Examines walls and covers of graphs and digraphs, latin squares, pairwise balanced designs with prescribed block sizes, ranks and permanents, extremal graph conception, Hadamard matrices and graph factorizations. This e-book is designed to be of curiosity to utilized mathematicians, machine scientists and communications researchers.

In diesem Lehrbuch finden Sie einen Zugang zur Differenzial- und Integralrechnung, der ausgehend von inhaltlich-anschaulichen Überlegungen die zugehörige Theorie entwickelt. Dabei entsteht die Theorie als Präzisierung und als Überwindung der Grenzen des Anschaulichen. Das Buch richtet sich an Studierende des Lehramts Mathematik für die Sekundarstufe I, die „Elementare research" als „höheren Standpunkt" für die Funktionenlehre benötigen, Studierende für das gymnasiale Lehramt oder in Bachelor-Studiengängen, die einen sinnstiftenden Zugang zur research suchen, und an Mathematiklehrkräfte der Sekundarstufe II, die ihren Analysis-Lehrgang stärker inhaltlich als kalkülorientiert gestalten möchten.

**Extra info for A 1/3 Pure Subharmonic Solution and Transient Process for the Duffings Equation**

**Sample text**

SHEN Table I. 1 density, velocity and pressure L 1 errors for the Godunov scheme with the exact Riemann solver and the new solver in different scales of grids. 321964E−3 Table II. 2 density, velocity and pressure L 1 errors for the MUSCL scheme with the exact Riemann solver and the new solver in different scales of grids. 808145 Table III. 3 density, velocity and pressure L 1 errors for the MUSCL scheme with the exact Riemann solver and the new solver in different scales of grids. 182284 Table IV.

These equations express conservation of mass and momentum. In conservative form, they are as follows: Ut + F(U )x = S U= h hu , F(U ) = hu hu 2 + 12 gh 2 , S= 0 (1) gh(s0 − sf ) where U is the conservative variables vector in which, h and u are flow depth and velocity, respectively; F(U ) the flux vector; S the source term vector, consist of bed slope S0 and friction slope Sf . 33 where n is the empirical Manning resistance coefficient. The governing equations are based on the assumptions of hydrostatic pressure distribution, incompressibility of water and a sufficiently small channel slope.

The source term consists of two parts, the bed slope and the friction slope. Treatment of each part will be explained separately. 1. Bed slope treatment The main subject in dealing with the bed slope is to balance it with the convection flux in each cell at stationary flow field. This will be explained in more detail under the C-property preposition [29]. The C-property will be explained and approved for the proposed algorithm later on, but first the details of the source term discretization are presented below.