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4
votes
1answer
52 views

Error implementing Robin boundary conditions in toy ODE problem

I am attempting to solve the following ODE problem: $$-u''+ u = x$$ $$u(0) = 0$$ $$u'(1) = -u(1)$$ The exact solution is: $u(x) = e^{-x-1} - e^{x-1} + x$ I have a Dirichlet at $x = 0$ and a Robin ...
0
votes
1answer
53 views

Dynamic problem Finite Element

Hi guys! I am working on a dynamics problem that I am not really sure how to solve it. Can anyone help me? The professor gave as a hint that we should compute the stiffness matrix of a linear ...
0
votes
0answers
22 views

Heat equation with Neumann B.C. in Maple

I have written the code in Maple for Heat equation with Neumann B.C. Could anyone check it? I will be very grateful! Heat equation: diff(u(x,t),t)=diff(u(x,t),x,x); Initial condition: U(x,0)=2*x; ...
1
vote
1answer
74 views

heat equation with Neumann B.C(explicit scheme) in Maple

∂u/∂t=α(x,t)*∂^2u/∂x^2+b(x,t) u(x,0)=f(x) Initial condition ux(0,t)=0 2nd type Boundary condition ux(1,t)=0 2nd type Boundary condition There is my code in Maple for the 1st type B.C. And I really ...
2
votes
1answer
196 views

Weighted Gauss-Seidel Algorithm

In Jacobi method's Wikipedia article there's a section that describes Weighted Jacobi method: http://en.wikipedia.org/wiki/Jacobi_method#Weighted_Jacobi_method. I need to implement the Weighted ...
1
vote
0answers
65 views

Characteristic length of differential element of cylinder surface?

I am trying to find the Nusselt number for a small element of the outside of a cylinder that has a height of $\Delta z$. I found the average Grashof number of a surface as $$Gr_{L}=\frac{\beta \rho ...
1
vote
0answers
95 views

Problem with cell size and boundary conditions in transient cylindrical conduction

I am attempting to model the steady state behavior of a cylinder using the finite volume method (FVM) subjected to a variety of boundary conditions in Matlab. First off, I am treating the cylinder as ...
0
votes
1answer
157 views

Finite volume method to determine steady state temp in cylinder

I am attempting to model the steady state behavior of a cylinder using the finite volume method (FVM) subjected to a variety of boundary conditions in Matlab. First off, I am treating the cylinder as ...
0
votes
0answers
56 views

Performing Finite Volume analysis and getting strange results [closed]

I am performing an unsteady conduction simulation of a cylinder in Matlab. The cylinder's bottom is insulated, its side is exposed to convection and its top is exposed to both irradiation, and ...
6
votes
1answer
65 views

Numerical iterative method, estimating error

Given iterative method: $x_{n+1}=0.7\sin x_n +5 = \phi(x_n)$ for finding solution for $x=0.7\sin x +5$, I want to estimate $|e_6|=|x_6-r|$ as good as possible, with $x_0=5$, where $r$ is exact ...
5
votes
3answers
120 views

Newton's method for a given polynomial

Let $f(x)=\frac{1}{5}x^5+\frac{1}{3}x^3+x-1$ Show that $f$ has only one zero $r$ in interval $(0,1)$ To find approximation of $r$ we apply Newton's method ...
1
vote
0answers
64 views

Prove $T_n(x)$ of Chebyshev Polynomial given the recurrence relation [closed]

Using the recursion formula for Chebyshev polynomials, show that $T_n(x)$ can be written as $$T_n(x)=2^{n-1}(x-x_1)(x-x_2)...(x-x_n)$$ where $x_i$ are the $n$ roots of $T_n$ The recurrence ...
0
votes
2answers
1k views

How to solve this system with conjugate gradient algorithm in matlab

CG Algorithm https://skydrive.live.com/redir?resid=E0ED7271C68BE47C!386&v=3 System of equations, the question and the example https://skydrive.live.com/redir?resid=E0ED7271C68BE47C!387&v=3 ...
2
votes
1answer
117 views

ode45 usage in this case?

The background is that I'm solving a problem in numerical analysis and I seem to be halfway having solved the non-linear system and now getting to the part where I should apply solving differential ...
0
votes
0answers
285 views

matlab program to calculate Maxwell-Boltzmann distribution

I am trying run a Matlab program to number density of Maxwell-Boltzmann statistics (non relativistic limit) $n= \frac{m^2}{2}\pi^2 \exp(\frac{-1}{T})K2(\frac{m}{T})$ where $K2$ is the Bessel ...
5
votes
1answer
143 views

Calculate large and small frequency separation for the Sun

I want to determine the big and small frequency seperation from timeseries data for the sun. An excerpt of the data (timeseries and power series) is plotted below. The power series is calculated in ...
2
votes
0answers
94 views

Prediction model on GPU [closed]

I am doing a small project at school. I have done my code implementations in CUDA and did some performance measurements with real values, i.e. running the program with different number of threads, ...
5
votes
1answer
148 views

Local truncation error and transformation of coordinates

I am given the advection equation $$ u_t=u_x $$ and then the transformation of coordinates $$ x=x(\xi,\theta), \qquad t=\theta $$ which leads us to the transformed equation $$ x_{\xi} u_{\theta} - ...
4
votes
2answers
419 views

2D Schrödinger time-independent finite difference and eigenvalues

I'm learning about numerical methods to obtain the eigenvalues of a system. I have to find the eigenvalues for the time-independent Schrödinger equation but I'm having some difficulties understanding ...
4
votes
1answer
533 views

TypeError from scipy.optimize.curve_fit

I am trying to fit a data set to an exponential model using scipy. However, the covariance matrix that is returned is 'inf' and I receive the following error: Traceback (most recent call last): ...
2
votes
1answer
47 views

Not Sure How to Solve A System Of Linear Equations In MAPLE13

How can one solve the following system of linear equations in MAPLE 13?I know how to solve a linear equation with one variable floating around but not this one. $$x-2y+3z=10$$ $$3x-2y+z=2$$ ...
4
votes
0answers
101 views

Solving diffusion PDE using finite differences

I need some hints on how to solve this diffusion equation ($\alpha, k_1,k_2$ and $k_3$ are constants): $$ {\partial P \over \partial y} + k_1 {\partial P \over \partial t} + \alpha P = {1 \over k_2} ...
0
votes
1answer
68 views

Thermoplastic Equation solving

I was given a problem by my professor as follows Solve the System $pV=S$ $pcT=kT+BS\frac{dG}{dt}$ $\frac{dS}{dt}=\mu(V-\frac{dG}{dt})$ $\frac{dG}{dt}=f(S,T)$ Where $p$, $c$, $B$, $\mu$ are ...
3
votes
1answer
136 views

multiplications of graph adjacency matrix

Suppose $A$ is a directed graph adjacency matrix. Is there any good interpration of the $(i,j)-$entry of the matrix $(A^{32}\cdot (A^T)^{32})$ ?
3
votes
2answers
136 views

How to prove that my problem is np-hard

For an assignment i need to program an application to schedule conversations. Something similar to speeddating or Pta meeting. The problem is that i know that this is hard to solve, but i dont know if ...
3
votes
1answer
745 views

Gauss-Seidel iterations node spacing

I am working on an assignment where I am determining the temperature distribution of a chip on a substrate. When I decrease the nodal spacing the results change drastically. The smaller the nodal ...
3
votes
2answers
172 views

How to establish that an iterative method can be applied to large matrices whose size may reach 10^3?

I have an iterative method for computing the Moore-Penrose generalized inverse of matrices, that is $$X_{k+1} = ((I-\beta X_{k}A)^t) + X_{k}$$ with initial approximation: $$X_{0} = \beta AA^t$$ ...
2
votes
2answers
1k views

Depth of a Binary Search Tree

I wrote a function to search a Binary Search Tree, but I have logic problems: When I insert some values, and I have a tree of 2 levels, and the final level (2 in this case) is not full (full is that ...
5
votes
2answers
207 views

Proving convergence of 5 point scheme for the Poisson equation

So, we are solving the Biharmonic equation ($\Delta^2 u = f$) on a rectangle by solving the Poisson equation ($\nabla^2 u = f$) two times. We have nice boundary conditions, $u = 0$ and $\Delta u = 0$ ...
12
votes
2answers
3k views

How to impose boundary conditions in finite difference methods

I have a problem when I want to use the high order center difference approximation: $$\left(\frac{-u_{i+2,j}+16u_{i+1,j}-30u_{i,j}+16u_{i-1,j}-u_{i-2,j}}{12}\right)$$ for the Poisson equation ...
-5
votes
1answer
327 views

Successive over-relaxation formation of heat equation?

What is the form of SOR iterative equation for the heat equation $u_{xx}=u_{t}-1$ using centered differences both in time and spatial derivatives and using Crank-Nicolson method? ...