Non-linear Definition and 340 Threads

Homework Statement Well I have conducted a regression analysis, and have plotted a graph of my residuals vs my input variable. I know that for a linear regression the residuals must be randomly scattered blahblah, but from this graph, it looks like it has a curve to it ? is this because I only...

Hi everyone. This is not a homework problem. I am very familiar with the case of linear(direction) friction. F_{friction}=\mu F_{normal} ...(1) However my question is closer to something like this: \tau_{friction}=\beta F_{normal} ...(2) Where \tau_{friction} is a torque Imagine if a...

Hello, I was wondering if anyone could shed some light upon solving this: s(x)'' = (a b s(x)) / ||s(x)||^3 Where s is a n dimensional vector, || || is operation finding the magnitude and a and b are constants. Is this solveable or will I have to use alternative numerical methods?

Out of boredom* I derived some simplified equations to describe the dynamics of a pneumatic gun. These equations are extremely simplified, but they should provide some insight into the system that my numerical models can't. This system had one non-linear equation that could be rewritten as the...

I was just thinking about this the other day... Given any 'blackbox' circuit, for which the values of the thevenin voltage and thevenin resistance are known. And given that a non-linear device is placed across the terminals of the circuit. What relation would one use to find the current...

Homework Statement If a delicate istrument havng a mas of 5 kg is placed on a springof length L so tha its base just touches the undeformed spring and then inadvertly released from the position, determine the maximum deflection xm of the spring assuming (a) linear spring constant k=3000N/m...

Hello, having a lot of trouble with a dodgy question one of my lecturers has set us before teaching us how to do it, none of my course can seem to work out what to do. The question is: dy/dx=(x(y+3)+(y+3)2)/x2 where y(1)=4, and x>0 I tried a substitution of z=y/x to eventually give...

Can someone please give me a hint to solve \frac{d^2x}{dt^2} = \frac{1}{x^2} It is not a homework problem, but something for fun. It looks simple but is the solution simple? thanks

Googling this has only given me fairly detailed scientific papers and wikipedia (unusually) doesn't come up. Does anybody have a cheap and cheerful definition? Deducing these terms literally is not risk-free, but I suppose it involves a Gaussian probability distribution N(mu,sigma) where mu and...

Homework Statement This problem shows up in Anton's Elementary Linear Algebra in the first chapter. It's one of the last problems, so I don't think that it is crucial for me to 'solve' it. But I would like to clear up some conceptual questions I have. First here is the problem...

Homework Statement \frac{dy}{dx}+2xy^{2}=0 I am stuck on this. I realize that this is a non-linear exact equation, but I just cannot wrap my mind around any type of method to attack this one. TIA for any help

Hello, Could anyone help explain why \partial/\partialx[K(x,u)\partialu/\partialu] is not a linear operator?

I've run across a PDE that (since I've failed to take a PDE class!) I'm finding some difficulty in solving. Does anyone have any suggestions? It's on a function R(r,t), with functions a(r,t) and b(r,t) and a constant k. If it's easier to solve with a and b not having t-dependence (just being...

I am new to non-linear PDEs. So I tried to solve it, but I stuck in the beginning. U^2_xU_t - 1 = 0 U(x, 0) = x

I am not able to find the general integral of the following non-linear 2nd order equation: y^2 y'' + a y^3 - b = 0 in which: y = f(x) 0 < a <= 1, is a constant b > 0 , is a constant.

Hi Consider a set of n non-linear equations and I have m unknowns and n<m, so I don't have enough equations to solve the problem. All the unknowns are parametrized by say t A possible solution to this that I considered was to take the derivative w.r.t. t and obtain another set of n...

I keep getting the error, NDSolve`FiniteDifferenceDerivative::aord: The approximation order 0 given for dimension 1 should be a positive machine-sized integer or Pseudospectral. I have a very complex and nonlinear pde to solve in mathematica and I keep getting errors with the code...

I am currently using a pulse generator with a reasonably fast rise-time (something like 1 ns) for some experiments. It works well as long as I am using e.g. 50 Ohm loads but the problem is that it can't source much current, meaning it doesn't work well for lower impedances. Now, my problem is...

Hey all, I'm cross-posting this in the materials and mechanical engineering section because I feel like this might be a good question for both places. I'm trying to develop a physical model of a mechanical system in MapleSim, and have the questions about the friction model used. This isn't a...

Hey all, I'm trying to develop a physical model of a mechanical system in MapleSim, and have the questions about the friction model used. This isn't a software question, but more trying to understand the math of a non-linear friction model. The model itself is a sum of the Coulomb friction...

Hi all-- I can't figure out how to approach the following difference equation: ax_{t}+f(x_{t-1})+bx_{t-2}=e_{t} where a, b are constants, e_t is a known function and f(x_t-1) is a convex, u-shaped function that goes through the origin. (Sorry Tex would not want to work) To begin with, I...

Hi, Does anyone knows how to solve this 2nd order non linear differential equation with exponential components? d"V/dx" = A*exp(-B*V)-C*exp(B*V) where A, B, C are constants. Thanks

Hope I have posted this in the right section, this question is half differential equation and half finite difference method. The equation I have is a form of the Lucas Washburn equation, which is concerned with capillary rise...

Hello, I'm a student from Lithuania. I have found in one forum topic your discussion about non-linear equation convertion into a linear form.. I have some problem with that...Could you help me, please? :) For, example, I have two non-linear models: 1. y = a [1/(1+b/(c+x))]*exp(-d*x) 2. y =...

I'm interested in coming up with an function that approximates the solution to a non-linear differential equation. (There is no known closed form solution) The equation is Y''=(1/Y)(Y')^2-Y*A+Y^2*A where "A" is a constant, and Y' and Y'' are the first and second derivatives with respect to...

could anyone help me with solving this second order differential equation? I am a noob on here so not sure how you get the mathplayer stuff on... so the equation is of the form x'' +ax' + bx^n = 0 (x^n means x to the power n, with a and b constants). i tried substituting x'=u to get a first...

hi, Do the addition of non-linear terms in action play any significant role in string theory?? if so, what is its significance in string cosmology? --- anuradha

Hey Guys, I am really confused about the first problem on my first problem set in Diff Eq (not auspicious is it? Oh well...) Draw the Direction field y' = y -y^2. Identify Isoclines and any equlibrium solutions. I don't understand how to approach this problem because doesn't the y^2...

Hi, I have a non-linear function F: \Re^{3}\rightarrow\Re. I would like to find the roots of this equation numerically, since an explicit formula cannot be derived. As far as I am aware Newton's method can only be utilized when the domain and the range of the function are of the same...

Dear All, I have maybe quite a naive question: Does there exist a result that a generic system of non-linear equations have a unique solution? (defined from R^n to R) Similarily as it exists a result that a generic square matrix could be inverted? Waiting impatiently for news...

Homework Statement I am modeling a set of equations for a protein network. It is a feedback loop between 2 proteins. I have gotten the differential equations for this model and plan on doing an extended Kalman Filter to estimate the levels of protein in real time. However, I am having...

Dear all, I have a set of 5 non-linear equations with highly complicated and long forms for which I wish to find the unique solution. I was going to tackle this problem with Broyden's method since the derivatives cannot be easily found. However, even if I get a solution from this, this is...

I don't know very much about DEQs, can someone point me in the right direction for solving this? Note: \phi is a function of another variable and C_1, C_2 are constants. -\phi ^2 \cdot C_1=\frac{1}{1+\phi ' ^2}+C_2 I have tried trig sub, but I didn't get anywhere. Regards...

Question on Newton’s Method of solving systems of non-linear equations. I understand the concept for a single non-linear y=f(x) solved for zero, but am confused about systems of non-linears. If I take two functions U(x,y) and V(x,y), am I solving for the points where they intersect with each...

infinite series solution for NON-linear ODEs? Is it possible to use the infinite series method (Frobenius) to obtain general solutions of non-linear ODE's, I want to try a second order equation. Any good references where I can see how that goes exactly?

Hello, I have the 2nd-order nonlinear ODE below: k(v)=\frac{\phi ''(v)}{\phi (v) (\phi ' ^2 (v) +1)^2} Where k(v) is some function. I would like to investigate for what functions k there can exist solutions on a given interval [a,b]. For example, if k(v)=0, then \phi '' (v)=0 which implies...

Hey folks, Does anyone have any experience with how to solve non-linear ODE's numerically, perhaps in mathematica?? I am trying to solve the following equations: 3H_a^2+3H_aH_b=K_1 \dot{H}_a+3H_a^2+H_aH_b=K_2 \dot{H}_b+3H_a^2+3H_aH_b=K_3 Where H_a and H_b are both...

Hey everyone, Having some trouble here using the solver we were supplied and modifying it to fit our problem... I have a wire with a current flowing through it. I'm trying to find the temperature distribution wrt. position in the wire. BV's are: T(x=L/2) = 300K dT/dx (x=0) = 0 (Apparently...

Hi all, At the moment I am trying to find a best fit equation to radial velocity data vs. time of a planet HD17156b. The paper with the Authors fit parameters (I am trying to mimic the fit) has the arXiv ref number of :0704.1191v2 From this paper I extract their data, which is on the final few...

I'm having trouble solving this differential equation: (2x^2)yy' = −1 I'm just really not sure how to go about solving this.

Hello everyone. My question is quite long, so please bear with me; my professor is very busy and cannot help me at the moment, and I can't contact the course tutor. We have the DE \ddot \theta + \alpha \dot \theta + \sin{\theta } = \epsilon \cos{\omega t} where theta is the angle the...

Now we've all been taught how to use the average. Let me give 2 examples to those who don't know. Example 1: Say an object moves with velocity 3t in the time t=0 till t=2. Find distance covered. Initial velocity = 0. Final velocity = 6 disp. unit/ time unit. Avg. Velocity = 3 disp...

http://img132.imageshack.us/img132/5153/njga7.jpg Question 8 is the question I need, but 7 has relevance for it. I have my equilibrium points, and am stuck on two of them with the same problem. 1 of my points (H,P) = (0,L) - No hunters, but prey. I put this into my jacobian matrix, and I...

Dear everybody, I wave an equation with datas and want to regress in non linear form with plot. Would you help me to solve the equation bellow by any softwares, please? The data, the equation and parameters are given bellow. I want to fit the data to non-linear equation to find Df and k...

Find the inverse of the (nonlinear) transformation from R^2 to R^2 given by u=3y v=3x^7-6y x=? y=? The Attempt at a Solution - I'm really not sure what to do on this problem. We haven't seen any problems even similar to it in class, so I'm looking for help on it.

I have 15 equations with 15 unknowns describing a dynamic process. I would like to know how I can conbine solving non-linear equations together with ordinary differential equations (1st and 2nd order) simultaneously, without using ode45, but Euler's method.

Hello, I am currently trying to design a system that will sychronize two propellor motors, and I must design using the following equation: w'*I + (w^2*r^2*p*S*C_d)/(2) = T_t + T_ss w' = Angular acceleration I = moment of inertia w = angular velocity r = radius of blade p = air density...

Homework Statement Obtain the fixed points for the following as a function of a, where 0<a<infinity: f(x)=tanh(ax) Homework Equations The fixed point is given by f(x^{*})=x^{*} The Attempt at a Solution It's basically a math problem: tanh(ax)=x Find x in terms of a. I tried it two...

Given that F(x,y)=xy(x+y-1). Determine whether S={(x,y) | F(x,y)=0} is a smooth curve. Now, F(x,y)=x2y + xy2 - xy Let gradient F = (2xy + y2 - y, x2 + 2xy - x) = 0 So 2xy + y2 - y = 0 and x2 + 2xy - x = 0 In order to determine where S is smooth, I have to solve these 2 equations for x and...

I want to first explain my current understanding and motivation so you guys can whip me into shape in case I'm misunderstanding the starting point -- SR and linear transformations. So, we can write the laws of electrodynamics in terms of the electromagnetic field tensor F^{\alpha \beta} as...