Finite difference Definition and 117 Threads

Hi guys , i am solving this equation by Finite difference method. (dt2/dx2 + dt2/dy2 )= -Q(x,y) i have developed a program on this to calculate the maximum temperature, when i change the mesh size the maximum temperature is also changing, Should the maximum temperature change with mesh...

hello. I have a MATLAB skeleton provided because i want to model a distribution with a circular geometry. all in all, i want the 3d graph of the code to be some type of cylinder. This is the code: % flat step condition for ii=1:nHi, for jj=1:nHj, if (X(ii)/R_P)<1 &...

Homework Statement Plot the transient conduction of a material with k = 210 w/m K, Cp = 350 J/kg K, ρ = 6530 kg/m3 Where the material is a cylinder, with constant cross sectional area and is well insulated. The boundary conditions for the cylinder: T(0,t) = 330K T(l,t) = 299K...

Hi, Are there any open source C or Fortran libraries for solving 3D Poisson'sequation on an irrefular domain? I'm having difficulty finding them. If not, is there any papers or recipes that would be useful so I could write my own? Speed is not a priority, I just need anything that works...

Hello all, I hope this is the write sub-forum for this question. I have been looking at the Laplacian of a 2-D vector field. It is explained nicely by this Wikipedia article here. My question is more regarding how these operators work together. So, in the case of the Laplacian, it tells me...

Hey! :o I have a implicit finite difference method for the wave equation. At step 0, we set: $W_j^0=v(x_j), j=0,...,J$ At the step 1, we set: $W_j^1=v(x_j)+Dtu(x_j)+\frac{Dt^2}{2}(\frac{v(x_{j-1})-2v(x_j)+v(x_{j+1})}{h^2}+f(x_j,0)), j=0,...,J$ Can that be that at the step 1 $j$ begins from...

Hi, I have to use a wide 5 point stencil to solve a problem to fourth order accuracy. In particular, the one I'm using is: u'' = -f(x + 2h) + 16f(x + h) - 30f(x) + 16f(x - h) - f(x - 2h) / 12h2 or when discretized u'' = -Uj-2 + 16Uj-1 -30Uj + 16Uj+1 -Uj+2 / 12h2 In addition to...

Hey! :o I am implementing in a program the finite difference method for the heat equation. The problem is the following: $$u_t(x,t)=(g(x,t)u_x(x,t))_x+f(x,t), \forall (x,t) \in [0,1]x[0,1]$$ $$u(0,t)=u(1,t)=0, \forall t \in [0,1]$$ $$u(x,0)=0, \forall x \in [0,1]$$ where $f(x,t)=\pi x...

Hello! :) I am implementing the finite difference method in a program in C and I got stuck at the rate of convergence.. The formula is \frac{log(\frac{e_{1}}{e_{2}})}{log(\frac{J_{2}}{J_{1}})} , right? where e_{i}=max|y_{j}^{J_{i}}-y(x_{j}^{J_{i}})| , 0<=j<=J_{i} . How can I find the J_{1}...

For possion equation $$u_{xx}+u_{yy}=f$$ I know the general five point scheme is in the form $$a_{1}U_{i,j-1}+a_{2}U_{i-1,j}+a_{3}U_{i,j}+a_{4}U_{i+1,j}+a_{5}U_{i,j+1}=f_{i,j}$$ But , is there have the form...

I have the differential equation \frac{dM}{dt}=4\pi \rho(r,t)r(t)^2\frac{dr}{dt} which is the first term from M(t)=4\pi\int_0^{r(t)}C(r,t)r(t)^2dr This describes the change in mass (M) of a sphere from a change in radius (r) given a density (rho) that depends on radius and time (t). My...

Homework Statement http://puu.sh/1QFsA Homework Equations The Attempt at a Solution I'm actually not sure how to do this question. How do i find Δx^2. I kind of understand the question but I don't know how to prove it. I know that Δy becomes dy when the width becomes...

Hi. I'm trying to determine the CFL condition for the fourth-order leapfrog scheme. I'm finding 2 as what's published, which does not match what I'm getting. Does anyone know where I can find a von Neumann (or Fourier) stability analysis of the leapfrog (2,4) scheme (so I can compare my work)...

hi; I have 3 hyperbolic electrodes ,one as a ring and 2 others as endcap electrodes which have potential v and 0 respectively.(quadrupole ion trap) I want to solve potential inside the trap by finite difference method. I don't know how general equations for unshaped materials will change...

Use finite difference method to solve for eigenvalue E from the following second order ODE: - y'' + (x2/4) y = E y I discretize the equation so that it becomes yi-1 - [2 + h2(x2i/4)] yi + yi+1 = - E h2 yi where xi = i*h, and h is the distance between any two adjacent mesh points. This...

Hi, I have a question regarding finite difference approximation: Consider the finite difference approximation u'(xj-1/2) + λu(xj−1/2) ≈ 1/h*[u(xj ) − u(xj−1)] + λ(θu(xj ) + (1 − θ)u(xj−1)) how can I Find the order of approximation as a function of θ? I am really new in this field, so...

Hallo, I tried to use 'finite difference' method to solve a Initial Value Problem(IVP). For the two boundaries I used periodical condtion and for the differential operators I used 4th degree center approximations. But as result, I got this thing. Where comes this strange oscillation What do you...

Homework Statement I'm doing a class on Numerical Solutions of DE and I have my first assignment. The problem is stated: Consider the following second order boundary value problem: \epsilon \frac{d^{2}y}{dx^{2}} + \frac{1}{2+x-x^{2}} \frac{dy}{dx}-\frac{2}{1+x}y = 4sin(3x), y(0) = 2, y(2) =...

Hello to everyone, while solving homework course Nanotechnology and Nanocomponents, I have encountered a problem in FD method that is applied in even potential. In my homework assignment it is explicitly said that it must be done only in x>0 part of the domain, where my problem starts with...

Hello, I need help writing a MATLAB program to solve a heat transfer problem implicitly. For some reason this is very confusing to me. The problem is stated below. Any help is greatly appriciated. Let me know if you need a little more info. I need to write a program to solve this...

Hello I want to resolve a nonlinear partial differential equation of second order with finite difference method in matlab. the equation is in the pdf file attached. Thanks

Hello all, I am in the process of solving a finite elements problem involving obtaining deflection of a simple mass-spring-damper 2nd order ODE system with a defined forcing function. While going through my class notes, I came across the idea of the central difference method, which is...

I have a system of non-linear coupled PDEs, taken from a paper from the 1980s which I would like to numerically solve. I would prefer not to use a numerical Package like MatLab or Mathematica, though I will if I need to. I would like to know if anyone knows how to solve non-linear coupled...

I made a small program to simulate the time development of a 1D wavepacket obeying the Schrodinger equation, mostly in order to learn a new programming language - so in order to not have to invoke big numerical methods packages, I opted for the simplest solution: The standard three-point...

I'm attempting to perform interpolation in 3 dimensions and have a question that hopefully someone can answer. The derivative approximation is simple in a single direction: df/dx(i,j,k)= [f(i+1,j,k) - f(i-1,j,k)] / 2 And I know that in the second order: d2f/dxdy(i,j,k)= [f(i+1,j+1,k)...

Hello all: For modeling flow (or whatever) in a non-rectangular geometry, can anyone comment on whether the finite element method would be better or worse or the same as the integrated finite difference method? I'm reading some papers by competing groups (so I can decide which code to...

Problem - Find backward finite difference approximations to first, second and third order derivatives to error of order h^3 Attempt By Tailor’s series expansion f(x-h) = f(x) - h f’(x) + h^2/2! f’’(x) - h^3/3! f’’’(x) + … Therefore, f’(x) with error of order h^3 is given by f(x-h) = f(x)...

I have a question which states that I have to solve Phi using the finite difference method in matlab. Phi = Phi_infinity - Phi_t where Phi_infinity = 1 - e^2 and Phi_t = A(t).B(e) A has the differential for dA/dt = -c^2. A and B 1/e.d/de(edB/de)=-c^2.B where e is a separation...

Given a partial differential equation, how would one go about implementing the forward finite difference method to the Taylor series?

Hello: I am looking to solve a set of 1D PDEs. I thought the finite difference method would be a good way to go about it. So I decided to pick a simple first order forward difference scheme to obtain preliminary results. I just have 1 question: According to my scheme, at the last node...

Hi Sorry for the stupid question, but what is exactly a "stencil" in finite difference methods ? Is the results of the expansion points ? Cheers Alex

I am writing a multi-region diffusion code. The two regions have different material properties, so the analytical solution shows a discontinuity at the interface between the regions. As can be seen here: The numerical code I am running is (Mathematica): While[converge > .00001...

Hey, I want to solve a parabolic PDE with boundry conditions by using FINITE DIFFERENCE METHOD in fortran. (diffusion) See the attachment for the problem The problem is that there is a droplet on a leaf and it is diffusing in the leaf the boundry conditions are dc/dn= 0 at the upper...

Hey, I want to solve a parabolic PDE with boundry conditions by using FINITE DIFFERENCE METHOD in fortran. (diffusion) See the attachment for the problem The problem is that there is a droplet on a leaf and it is diffusing in the leaf the boundry conditions are dc/dn= 0 at the upper...

What is a finite-difference discretization for the partial differential term: \frac{\partial^4\phi}{\partial x^2\partial y^2} Thanks in advance.

Hi, We all know that the finite difference formulae for the derivatives are given by: \frac{dy}{dx}_{i}=\frac{y_{i}-y_{i-1}}{\delta x} and \frac{d^{2}y}{dx^{2}}=\frac{y_{i-1}-2y_{i}+y_{i+1}}{\delta x^{2}} What would be the formulae for the boundary terms? when i=1? I think I can...

Homework Statement I have to program a three component decay chain using finite difference approximation. I understand finite difference and have written my code, but I have an error I can not find which is giving me an erroneous answer. The curve is correct, but the magnitude of the...

I know this is really stupid and it looks like i haven't tried at all but i am genuinely confused about this so any guidance at all would help big time. so here is the question. A steel bar, 70mm long is struck at one end by a heavy mass moving at 20m/s. The impact causes a compression wave...

Hi, I'm here for help and hope somebody could give a hand on this because I'm noob in this. I'm now constructing a MATLAB program to find Electrical field and potential within a square grid mesh with square cavity inside. like the picture above. I only manage up to this...

1-D Conduction+Convection::Deriving a Finite Difference Scheme ***For those of you who would like to skip the derivation of the energy balance, skip ahead to the bold subheading below where the actual Finite Difference Scheme begins*** I am trying to derive a finite difference scheme for...

------Question------ a) Research the three finite difference approximations mentioned above (forward, backward and central). Use a spreadsheet to demonstrate each of these numerical methods for the function below. y=x3 −x2 +0.5x Investigate the derivative over the range x = [0,1], using...

Hi, i need help in solving a Fick's Law [ (∂c_k)/∂t = D_k (∂^2 c_k)/(∂x^2 ) ] by Finite Difference Method. Previously, I tried solving the Fick's Law by using the Separation of Variable method but that was not the correct way as told by my Prof as the correct way is to use Finite Difference...

ive been given this question for a uni assignment: given the function: f (x) = 5(x^1.3) +1.5(7x − 3)+ 3(e^− x) + ln(2.5(x^3)) find the first derivative at all possible points within the interval [0, 6], with step length h = 1 for: forward difference aproximation, backward difference...

Hello everyone: I am a C++ newbie; I am interesting in using C++ in my work on coupled fluid flow-chemical reaction problems. I apologize in advance for what is probably a very simple question. I would very much appreciate any help to get me on the right track! My goal is to come up with...

How do I use the finite difference method with M = N = 20 to obtain a plot of the solution of \nabla2u = 1, 0 < x < 1, 0 < y < 1, u(x,0) = x(1-x), u(x,1) = x(1-x), 0 \leq y \leq 1, u(0,y) = 0, u(1,y) = 0, 0 \leq y \leq 1.

Hello everybody! I am trying to construct the FDFD method for 3D structures. I have already constructed the general formulation and specifically I have set the complete matrix form. Due to the fact that the matrices are too sparse, and my system is out of memory, I am trying to set the problem...

Hi I am trying to solve a nonlinear differential equation with the use of the finite difference method and the Newton-Raphson method. Is there anyone that knows where I can find some literature about the subject? I am familiar with the use of the finite difference method, when solving...

Hi The equation is: \frac{dP}{dt}-A*\frac{{d}^2P}{dx^2}-B*\frac{dC}{dt}=0 dP/dt=A*d2P/dx^2 was solved using a finite difference method. If the function C(x,t) is known, is it possible to solve the whole equation by using the finite difference solution as a supplement to the complete solution...

I'm going to take a finite difference linear and non-linear PDE course next semester. I'm wondering how enjoyable the material is, and how difficult it may be. I'm actually looking forward to the fact there may only be one test throughout the semester, if any, and it's a mid-term. The rest of...

http://e.imagehost.org/0218/question.jpg I think I've managed to create the finite difference equation in part a), but I'm not sure how to turn this into a matrix equation. Any advice would be appreciated!