# Tagged Questions

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### Book for ODEs and numerical solution

I would like to ask you information for a book. I want to (self) study ordinary differential equation and their numerical solution (with MATLAB). I am not a math student (life science) so I want a ...
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### infinitisimal part and the directional integral

In the paper A circle detection approach based on Radon Transform by Erman Okman and Gozde B. Akar. I have a few questions on some basics. first of all what does $$ds^2 = dx^2 + dy^2$$ ...
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### Relative error when computing derivatives via FFT

I want to compute a discrete derivative via the FFT. This amounts to multiplication by the wave number in Fourier space, as detailed in the stack exchange answer here. When I increase the ...
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### implicit non-linear equations with complex variables

I am trying to understand a methodology for solving implicit non-linear equations with complex variables. I would like to solve for z1 below where z2 is known. Also both z1 and z2 are complex ...
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### Anyone recognize this pattern? Plotting relationship between two parameters and their response.

First time asking a question here so hopefully I can provide enough information to you guys without explaining more than necessary. I'm doing some amateurish numerical analysis in MATLAB on some ...
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### How to solve this complicated differential equation?

I need to know how to solve this complicated differential equation in $z$ either analytically or numerically : \begin{eqnarray} \frac{dx_1}{dz} &=& -ib_1x_1 - ikx_2 \\ \frac{dx_2}{dz} ...
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### Solving solely continuous system of ode's with matlab

I'm working with the numerical integration of the system of differential equations, $\dot{x}=f(x)$ with the vectorfield, $f(x)$ being solely continuous. Examples of the systems which I'm working on ...
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### Change MATLAB code from Lax-Wendroff to Leapfrog

I want to see how leapfrog would look using this code, but I'm having issues implementing it. I think my biggest problem is adding in the $U_j^{n-1}$ term, I just don't get the logic. Here's what ...
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### Numerical Differentiation using Numerical Methods

I am currently studying Numerical Differentiation in MATLAB using Numerical Methods in Engineering with Matlab by Jaan Kiusalaas, and I am stuck at exercise 13 from Problem Set 5.1 from Chapter 5 ...
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### The definition and meaning of “machine epsilon” in MATLAB

I am taking a introductory course in numerical mathematics, using MATLAB and a numerical math text that refers to MATLAB often. In the text, the machine precision is defined as: The distance ...
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### What is wrong with this algorithm [closed]

Crout factorization: n=10 A = full(gallery('tridiag',n,-1,2,-1)) i = 2:(n-1); bmid = i.^2 / ((n+1).^4) b = [1+1/(n+1)^4, bmid, 6+(n^2)/(n+1)^4]' for i = 1:n L(i,1) = A(i,1) end for j = 1:n U(1,j) = ...
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### Backward error for Crout factorization

Ok, can someone please tell me what is the formula for the max error in LU decomposition of Crout factorization?
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### Gauss Seidel iteration in matlab

I've posted this question before for crout factorization. Now, I need help with Gauss-Seidel iteration. Write a program that takes a value for n and solves for x using the following method: ...
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### How can I solve an ODE when $F(x_0)=F'(x_0)=0$ is given at an unknown point $x=x_0$ using bvp5c?

I'm attempting to solve the following ODE using MATLAB bvp5c. I've used bvp5c for other typical multipoint boundary value problems but I have no idea how to deal with ODEs with conditions given at an ...
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### (newbie) spectral derivative

I have data that form a scalar field on a 2D grid, evenly spaced. The grid has a finite size. There is no particular periodicity patern in my data. I want to calculate the value of the gradient at ...
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### Matlab ode45 numerical solution

I'm trying to solve a 2nd order differential equation, using the Runga Kutta's ode45 function in Matlab. It's for a bachelor project, where I'm trying to simulate the behavior of a spherical robot, ...
49 views

### A numerical inverse Fourier transform

I am doing an research in phase noise, And I'm troubled in a paper. In that paper,it says when perform a inverse Fourier transform on ...
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### Ordinary differential equations with signed first derivative

Consider the following coupled set of ordinary diferential equations: \begin{align} (K_{pa}+K_r)y_1(t)-K_ry_2(t)+C_0\operatorname{sign}(\dot{y}_1(t))\lvert\dot{y}_1(t)\rvert^\alpha &= ...
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### How to approximate a smooth function

Now I have a target smooth function f which is infinitely differentiable over $R^d$, $f \in C^{\inf}(R^d)$. $f = \Sigma c_ig_i(x)$, where $c_i$s are unknown coefficients and $g_i(x)$ is a smooth ...
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### Interest Rate Tree in Matlab

I would like to calibrate a interest rate tree using the optimization tool in matlab. Need some guidance on doing it. The interest rate tree looks like this: How it works: 3.73% = 2.5%*exp(2*0.2) ...
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### Best optimizer in Matlab for this problem?

I need to do yield curve extraction for fixed income. I have 10 fixed income instruments for which I have values. The method is called Nelson-Siegel Method: ...