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1
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1answer
69 views

System of nonlinear equations in MATLAB

I've got some problems solving (numerically) this system of equations. \begin{array}{l} 40 \cdot \cos (2t) + 105 \cdot \cos ({\theta _3}) - 75 \cdot \cos ({\theta _4}) - 91.924 \cdot \cos ({337.62}) ...
2
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0answers
50 views

Estimating eigenvalues from time-dependent non-linear operator

I have a very sparse non-linear system $N(u) = 0$ that can be solved as a time-dependent ODE, $\frac{du}{dt} = N(u)$, and explicitly integrated until $\frac{du}{dt} = N(u) = 0$, e.g. by forward euler, ...
0
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1answer
972 views

How do I extrapolate data from a NON-LINEAR (logarithmic) standard curve in Excel?

I have made a standard curve. The X-axis is logarithmic. The y-axis is linear. I have added a logarithmic trendline (y = -1.546ln(x) + 39.254; R² = 0.9906). How can I re-arrange the equation to ...
3
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1answer
71 views

How to pick a basis for the result of a non-linear function given a basis for its argument

I am trying to represent the result of a non-linear function in a small basis, given another small basis that does a good job a representing the argument of the function. More specifically, there ...
5
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3answers
437 views

Convergence of fixed point iterations of a non-linear matrix system

I'm working on modeling two phase immiscible flow in a porous medium. When I setup the system of equations, I obtain a non-linear system of equations that can be expressed in the form: $A(x)x=b$ ...
6
votes
2answers
698 views

Solution of quartic equation

Is there a open C-implementation for the solution of quartic equations: $$ax⁴+bx³+cx²+dx+e=0$$ I am thinking of an implementation of Ferrari's solution. On Wikipedia I read that the solution is ...
8
votes
5answers
311 views

Iterative solution to a nonlinear equation

I appologize in advance if this question is silly. I need to compute the root of \begin{equation} u -f(u) =0 \end{equation} Where $u$ is a real vector and $f(u)$ is a real-vector valued function. ...
7
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2answers
228 views

Basin of attraction for Newton's method

Newton's method for solving nonlinear equations is known to converge quadratically when the starting guess is "sufficiently close" to the solution. What is "sufficiently close"? Is there literature ...