Finite difference Definition and 144 Threads

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...

Hello, I have a homework of implementing finite difference solution of Hamilton-Jacobi equation using Matlab. The instructor is using her own set of notes. I'm a bit lost in details of the formulation (basically I want to learn more about the concept of characteristic curves, the merits of using...

Homework Statement I have this situation. A fluid is at rest at t=0 then a constant dp/dz = 10 is applied. Fluid starts moving. Homework Equations dV/dt = -(1/rho)dP/dz + viscosity*[1/r(d/dr(rdV/dr))] Initial condition t=0 dp/dz=10 boundary condition1 r=1 V=0 boundary condition2 r=0...

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...

Hi everyone. I developed a Matlab program to solve the diffusion equation, a partial differential equation, using the finite difference method. I solved it first with boundary conditions of C = 0, at x=0 and C = 0, at x = 1. I now want to change the boundary condition C = Co (some constant)...

Homework Statement how can i solve this problem by MATLAB? pls help me A (d4y/dx4) - B(d2y/dt2) = Cy A=E*I B=p*sin(w*t) c=p*w2 conditions are 1.at x=0, dy/dx=0 2.at x=0,y=0 3.at x=L d2y/dx2=0 4. at x=L d3y/dx3=p (p is a function of t here) x=0 and x=L...

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...

1. I have problem numerical solving of PDE with finite difference method in fortran. it is about optical fibers. At the beginning of the fiber the delta impuls is inserted, and I need function at the end of the fiber. 2. The equation is given in attachement as the code in fortran...

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...

Hi, I'm currently writing a code to solve a steady-state boundary problem across multiple layers of a system. The system involves diffusion-reaction of various species in a porous medium. I am simply using central finite differences to model this setup, which says that essentially -div*J+Q = 0...

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.

I need to solve the following PDE: \frac{1}{2}F_{\eta \eta }\sigma _{\eta }^{2}\eta ^{2}+\frac{1}{2}F_{pp}\sigma _{p}^{2}+F_{p}k(m-p)+F_{\eta }a\eta -rF=0 \label{6} where p goes from minus to plus infinity and eta goes from zero to plus infinity. Here p and eta are state variables and all...

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...

Homework Statement I have uploaded the problem statement and corresponding programs. Reader is the problem statement Reader1 is another file that is suppose to help Homework Equations I'm just having trouble getting started. I can do the analytical part on paper, but I don't know...

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!

To the moderator: please move this to the section on differential equations if you think it would be better there. I'm looking at a reaction-diffusion equation of the form \frac{\partial u}{\partial t} = \frac{\partial^2 u}{\partial x^2} + f(u), where, e.g., f(u) = u(1-u) for the...

Hi, I have a project for heat transfer, I know what I want to do but I don't know how to do it on Matlab. My assignment is attachment 1 - project.pdf The first part I have done (attachment 2 - computer project.pdf) I know I should be using the Matrix Inversion Method, but as I need...

Fiber Grating Using Finite Difference Method I have to solve the Fiber grating coupled-equations using FDM. These equations are coupled each other and strange inital conditions. That means ode45 from the MATLAB library function doesn't work here! I am totally fresh in numerical analysis...

Nodal Method?? What's the benefit of using Nodal method instead of finite difference method in solving a diffusion problem?

how can i develope second order Fromms difference scheme by using these points: (i-2, i-1, i , i+1) Please help me.

Hello, I'm currently doing some research comparing efficiency of various programming languages. Being a user of Matlab, Mathematica, and Excel, c++ is definitely not my forte. I was wondering if anyone might know where I could find a simple, standalone code for solving the 1-dimensional heat...

Hi all. Can someone briefly explain the difference between finite difference methods and spectral methods? What are their principles? And what is pseudo-spectral method?

Hi: I need some assistance or feedback on a Matlab program that I working on by applying the method of finite difference to calculate and output the steady state space distribution of temperature and resulting rate of hear flow in an I Beam made of Duralumin. I have written a partial code...

1) Using a similarity variable, the boundary layer equations for a two-dimensional, incompressible flow over a flat plate can be written below: 2f'''+ff''=0 The boundary conditions are: a) f ' (0) = 0, no slip at the wall b) f(0)=0, solid wall c) f ' (n) goes 1 as n goes infinity...

1) Using a similarity variable, the boundary layer equations for a two-dimensional, incompressible flow over a flat plate can be written below: 2f'''+ff''=0 The boundary conditions are: a) f ' (0) = 0, no slip at the wall b) f(0)=0, solid wall c) f ' (n) goes 1 as n goes...

computer engineering and mathematics,do you understand both of them?if u understand pls meet me.ı have a homework contains MATLAB course.ı can not write a program

:confused: my question y''(t)=-exp(-2t)+5y(t) accuracy on 5*10^(-3) by finite difference method and this question's MATLAB program. is there anyone who can do it ? it is very important for me.ı can not do and write a program in matlab.ı am a student ,my department is mathematics but ı can not...

I am curious to know if anyone has a program that will solve for 2-D Transient finite difference I have an assignment in a heat transfer class and I am supposed to use Matlab to solve for this. The governing equation (given in the attachement) is to solve using finite difference method using...

I am curious to know if anyone has a program that will solve for 2-D Transient finite difference I have an assignment in a heat transfer class and I am supposed to use Matlab to solve for this. The governing equation given here is to solve using finite difference method using matlab. In...

Difference Equation Hello, can anyone offer any insight on this equation? . I am very very rusty on solving this type of equations. a_{n+1} - a_{n} = n^2

Hello there...I'm currently stuck with a problem regarding finite differences. The question asks for me to come up with an equation to find the constant of the finite difference. An example would be...Let's take the equation y=10x^4 and the constant is 240. Any hints as to where to start or...

We have been given a program that can solve the following equation using finite difference methods: - \epsilon \left( \frac{\partial^2 \phi}{\partial x^2} + \frac{\partial^2 \phi}{\partial y^2} \right) - \frac{\partial \phi}{\partial x} = \sin \left(\pi y\right) \quad x,y \, \in \, (0,1) This...

I am finding (▲^2 - x▲)(x^3). I hope I am correct here... (▲^2 - x▲)(x^3) = ▲^2(x^3) - x▲(x^3) = ▲▲(x^3) - x( (x+1)^3 - x^3 ) = ▲( (x+1)^3 - x^3 ) - x( (x+1)^3 - x^3 ) = (x+2)^3 - (x + 1)^3 - (x+1)^3 +...

I am trying to find the ▲cos x. By using its definition. It simply turned out to be cos(x+1) - cos(x). How do I express this in terms of sine? (and as only one term)?

Hi, I am in an undergrad numerical analysis course. Our instructor lectured on some material not found in the book. Specifically, he talked about a way to check stability of finite differencing schemes (for PDE) by studying how each Fourier mode evolves in time. Then you can find an...

I am curious to know if anyone has a program that will solve for 2-D Transient finite difference. I have a project in a heat transfer class and I am supposed to use Matlab to solve for this. However, when I took the class to learn Matlab, the professor was terrible and didnt teach much at...