The one-dimensional heat equation ut + a ux = :0 is discretised using the forward Euler time scheme and a two node centred spatial scheme. This discretisation results in the following equation ● n+1 ui – u? At a n+1 Ui+1 - n+1 ui-1 24x Check the consistency of the discrete equation and state the order of the truncation error for At and Ax. Using the modified equation method, investigate the stability of the discrete equation. Comment on any stability limitations in terms of choice of At Comment on the implications of this scheme with regards to numerical diffusion and dispersion, if any.

The one-dimensional heat equation ut + a ux = :0 is discretised using the forward Euler time scheme and a two node centred spatial scheme. This discretisation results in the following equation ● n+1 ui – u? At a n+1 Ui+1 - n+1 ui-1 24x Check the consistency of the discrete equation and state the order of the truncation error for At and Ax. Using the modified equation method, investigate the stability of the discrete equation. Comment on any stability limitations in terms of choice of At Comment on the implications of this scheme with regards to numerical diffusion and dispersion, if any.

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

See similar textbooks

Similar questions

How do you derive the Kinematic Differential Equation of the Euler Parameters? I just want to know how we get the final matrix. For e4dot, e4 = (1/2)sqrt(1 + C11 + C22 + C33), e4dot = (1/4)*(1 + C11 + C22 + C33)^(-1/2) * (C11dot + C22dot + C33dot). From the C11dot, C22dot, and C33 dot equations we get e4dot = -(1/2)*(w1e1 + w2e2 + w3e3). I get how to get e4. How do I get the other 3 Euler Parameters? Please give detailed steps. The final equations should look like the image.
how can i solve this problem using professor's suggestion
The types of scaling transformation are stretch and enlarging O uniform and nonuniform O miniaturizing and enlarging O non of the above
The data base of B-rep. model contains of O topology O dimensions O geometry O topology and geometry
An automotive V6 engine consists of six identical cylinders for the engine to perform its intended functions. All the six cylinders must be operationally successful and the mileage to failure of a cylinder can be modeled with the Weibull distribution with shape parameter 1.5 and characteristic life 3.5x106 miles.Calculate:(a)The reliability, R (t) of the engine. (b) The failure rate, h (t) of the engine. (c) With your expertise as a quality reliability engineer, how would you achieve a product life cycle in typical manufacturing industry?
A small mixing tank with a long discharge line is attached to an input source pump: R1 R2 C Ps I a) Develop the Transfer function for the height deviation as result of a supply pressure deviation: H(s) as a function of the linearized resistances, the tank capacitance, and line inertance. When P,(s) modeling this, assume that the resistance and inertance are both throughout the lines such that the same pressure drop is across R2 and I. (Note, this can also be modeled using an equivalent electrical circuit where I and R2 are in series)
Solve the initial value problem below using the method of Laplace transforms. y"- y' - 30y = 0, y(0) = - 1, y'(0) = 49
You have a 1-D steady-state conduction problem, constant thermal properties, with energy generation q_dot. The material is 4.0 cm thick and has a constant thermal conductivity of k = 65.0 (W/m-k). The temperature distribution within the object is: T(x) = a + bx^2 a = 100 Celcius b = -1000 Celcius/m^2 Starting with the Heat Diffusion Equation and using the data given above, determine the following: • Determine the heat generation rate q_dot within the wall. • Determine the heat flux q" at x=0 and at x=L.
ent #damping- Sear X dynamics systems questions 1[1 X + To File C:/Users/40332698/AppData/Local/Packages/microsoft windowscommunicationsapps_8wekyb3d8bbwe/LocalState/Files/50/145/Attachments/dynamics%... + ? A Read aloud Add textDraw Page view Highlight Erase V Q 2/60 At time t = 0, the position vector of a particle mov- ing in the x-y plane is r = 5i m. By time t = 0.02 s, its position vector has become 5.1i+ 0.4j m. Determine the magnitude vav of its average veloc- ity during this interval and the angle 0 made by the average velocity with the positive x-axis. Type here to search O Bi 2 € P T 9°C Cloudy D4 ^ Je e F2 end prt sc F10 delete E 3 E I IL C D sex $ R F + 2 5 T G B A 6 Y H BR & 7 N Å U J FB * 8 M 1 F9 K ( 9 O ) O L home P - : ; F12 { + 1 insert e 1 -
Which one is the linearized modelling equation of the given system. 5-3Nm Your answer: O 22 + +72= fa(t) O2+6+11r fa(t) O 2+62 +9r= Ja(1)
Solve the heat equation u, = 0.2u on a digital computer using XX the Crank-Nicolson scheme. for the initial condition and boundary conditions TABLE P4.1 Case 1 2 3 4 5 Number of Grid Points 11 11 16 11 11 (x,0) = 100 sin TX L 0.25 0.50 0.50 1.00 2.00 L = 1 u(0,t) = u(L,t) = 0 Compute to t = 0.5 using the parameters in Table P4.1 (if possible) and compare graphically with the exact solution.
I need a clear step by step answer please with the simplest method :) Thank you