The Choice Of SL2 : Questions And Analysis

As already mentioned, distributed (modularized) models are solved by a set of partial differential equations due to all the dependent variables consist of more than one independent variable. However, these equations can be homogeneous or non-homogenous (inhomogeneous) equations. In practice, the solution of a homogeneous equation with the appropriate boundary conditions illustrates the behavior of the system after it has been properly set in motion and then subject to no further force. In addition to this, the solution depicts the trend of the system to vibrate at a number of natural frequencies. On the contrary, the solution of a non-homogeneous equation depicts the behavior of the system to specific forces (Holroyd, 2007).

Submission: The report from part 4 including all relevant graphs and numerical analysis along with interpretations.

7. The kinetic graph was correct as my hypothesis. My potential graph did not start in the same position as my data graph.

3) What do the rate of change values you just calculated represent? Why are some positive and some negative?

by the Trapezoidal rule is Etrap = O(h2 ) and by Simpson’s rule is ESimp = O(h4 ). i) For each of these numerical integration rules, what conditions are required on the integrand f so these error estimates are valid? ii) Suppose that the error using h = 5 × 10−3 is E0 = 1.19 × 10−4 when using either the Trapezoidal rule or Simpson’s rule. For both rules, ˆ estimate the error if an interval width of h = 1 × 10−3 is used. iii) The Matlab command [z, w] = gauleg(N); calculates the N Gauss-Legendre nodes z and weights w for the interval [−1, 1]. Show how z and w can be used to numerically calculate

The below figure indicates the 5 values I’ve chosen for K between 0.5 and 1 and shows how smooth the transition is from the original value to 1.

\KwIn{nodal value of solution $\mathbf{u} = \left(p, \mathbf{v} \right)$, volume geometric factors $\partial (rst)/ \partial (xyz)$, 1D derivative operator $D_{ij} = \partial \hat{l}_j /\partial x_i$, model parameters $\rho, c$}

σ_(R_X )=√(((∂R_X)/(∂V_1 ))^2 〖σ_(V_1 )〗^2+((∂R_X)/(∂V_2 ))^2 〖σ_(V_2 )〗^2+((∂R_X)/(∂I_D ))^2 〖σ_(I_D )〗^2+ ((∂R_X)/(∂R_S ))^2 〖σ_(R_S )〗^2 )

Step 2 Each step has a length of 10σ/N and identify the mid-point of each interval µ-4.9σ, µ-

now find the range of values which Kc can take for the overall system to be stable.

You should consider each of the four solutions and explain what happened using the terms "hypertonic" "hypotonic" and "isotonic."

First we define some important concepts. A stochastic process (c.q. probabilistic process) is defined by a T-dimensional distribution function.

. According to (Gomes , et al., 2013) the three main mathematical encounters with SIMP method are mesh dependency, checkboard patterns and local minima. To compensate for mesh-dependency and checkboard patterns instabilities, a well-known sensitivity filter brought forth by Bendose Sigmund is used (Gomes , et al., 2013). The local minima problem is dealt with by a continuation method with various increments in the function of the given filter (Gomes , et al., 2013). Pertaining to Bendose and Sigmund, the stiffness gained from SIMP model can be grasped as the stiffness of structures consisting of void and a quantity of solid material for the given density of the structure’s material (Zhu, et al., 2016). Because of the simplicity of SIMP

In this paper we will implement one of these methods, namely, homotopy perturbation method (HPM) which was firstly presented by He

Many physical phenomena in stationary condition such as electrical and magnetic potential, heat conduction, fluid flow and elastic problems in static condition can be described by elliptic partial differential equations (EPDE). The EPDE does not involve a time variable, and so describes the steady state of problems. A linear EPDE has the general form as presented in Eq. (1), where a,b,c are coefficient functions, the term f is a source (excitation) function and u is the unknown variable. All of this function can vary spatially (x,y,z).