# Tagged Questions

Questions on the symbolic (DSolve, DifferentialRoot) and numerical (NDSolve) solutions of differential equations in Mathematica.

240 views

### When plotting vector fields what is the difference between the following?

I am a new Mathematica user, and I have run into a question. What is the difference between the output of the commands: ...
416 views

### Problem when defining function through NIntegrate and NDSolve and Interpolation - Bug?

More than a single question, I have some doubts about the output of certain functions when defined through the result of other calculations. I am an active user of Mathematica, but maybe I haven't ...
550 views

### Solve ODE $d^2u/dx^2 + u/A = 0$

How can I solve following ODE with Mathematical: $$d^2u/dx^2 + u/A = 0 \quad (\text{or } \ C),$$ with the conditions: $$\left.\frac{d^2u}{dx^2}\right|_{x=0} = 0,$$ $$u(x=0) = B$$ and ...
175 views

### WhenEvent “StopIntegration” problem

The first example on the WhenEvent help page is ...
176 views

### NDSolve with Table and Boundary Conditions

I am trying to implement a 1D model of coupled field equations where I split up space into pieces to get a system of coupled ODEs which I call Eeqns and Ieqns. The problem I can't figure out is how to ...
247 views

### How do I plot the differential of this function?

Suppose I have this function: $$z(x,y) = \left| \frac{ \frac{1}{3x +iy} -2x}{iy + \frac{1}{x}} \right|$$ I want the contour plot of $\frac{\partial z}{\partial x}$ with axes $(x,y)$. Tried this ...
193 views

### How do get an output table or a plot of individual variables from NDSolve output

I have the following equations and settings: ...
49 views

### How to fit data with numerical solution of system of parametric ODE? [duplicate]

I need to find the parameters (k1,k2,k3,k4,k1r,k2r,k3r,k4r) that fit my data (list of [Intensity, time]) using the function ...
4k views

### Numerically solving Helmholtz equation in 2D for arbitrary shapes

I would like to solve the Helmholtz equation with dirichlet boundary conditions in 2 dimensions for an arbitrary shape. (for a qualitative comparison of the eigenstates to periodic orbits in the ...
40 views

### How can Mathematica solve 7 equations and want to find 7 variables [duplicate]

I have 7 equations as below * e1 := (1 - a) p Subscript[A, 0] Subscript[s, K ] ! *SubsuperscriptBox[(s), (L), (-a)] = (1 - b) Subscript[B, 0] (1 - Subscript[s, K]) (1 - Subscript[s, ...
247 views

### How to get solution from DSolve

How to get the solution from DSolve in such way that there is no need to copy the result. When for example solving: ...
274 views

### NDSolve fails to solve vector-valued function x'[t] == a . x[t] + u . b

I get no solution when I run the following command: ...
847 views

### Can NDSolve handle discountinuos data?

It is possible to numerically solve a differential equation if not-smooth data are involved? For example the following instruction return the error NDSolve::bvdisc: ...
314 views

### Partial Differential Equation in Parallel

is there any native way to implement multi-core parallel solving of PDE in Wolfram Mathematica? WM 10 now supports Finite Elements Method, but it is actually useless without parallelization. Usually ...
177 views

### NDSolve: EventAction list specification using Table fails

I have an NDSolve problem that needs a list of a large number of events that are generated programmatically. Here is a simple example that demonstrates the problem on Mathematica 7 and 8 (the versions ...
247 views

2k views

### Symbolic solution(s) to generalized Heat equation

Symbolic solution(s) to Heat equation? or more generally,(eventually) Green functions to known PDEs I am interested in variations of the heat equation: or more generally or even more generally ...
120 views

### DSolve breaks when the ordering of independent variables aren't proper?

Bug introduced in 5.2 or earlier and persisting through 10.4.1. I encountered this when trying to solve this problem with DSolve: ...
243 views

### Use NDSolve to solve a PDE

I have the following PDE (a master equation, and $P$ is probability density, $0\le x\le1$ and $0\le y\le1$): $$\partial_t P(x,y,t)=x\partial_xP(x,y,t)+(1-y)\partial_yP(x,y,t)+2P(x,y,t)$$ The ...
645 views

### Should DSolve always return solution with constant of integration?

Bug introduced in 10.0.0 and fixed in 10.0.2 Clear[y,x]; DSolve[D[y[x], x] - y[x]^2 + y[x]*Sin[x] - Cos[x] == 0, y[x], x, GeneratedParameters -> C] or ...
158 views

Following the fundamental theorem of algebra, I can (as stated here in Sec. 1.1.4) factor an $n$th-order linear ordinary differential equation $$a_n \frac{d^n x}{dt^n} + a_{n-1} \frac{d^{n-1} ... 0answers 370 views ### Speeding up NDSolve for system of differential equations I am wondering if there is a way to speed up this function that solves a system of ordinary differential equations with NDSolve? Thus far I've tried specifying a few different methods such as LSODA, ... 0answers 136 views ### Apply IC and BCs on Second - Order Linear PDE I am now trying to solve second - order linear partial differential equation in that interested eq. has been separated into variables to simplify the procedure for Mathematica. Here is my equation; ... 1answer 203 views ### Why DSolve giving Inconsistent or redundant transcendental equation on this problem Kamke's differential equation #574 has a solution, but Mathematica generates an error message as it tries to solve it. It still gives the solution. My question is: What could have caused Mathematica ... 1answer 214 views ### How do I subtract two contours? Suppose I have this contour described by the equation the root z of this equation$$ \frac{1}{x^2 + y^2} + \frac{1}{xz} = 2y $$Now suppose the equation is tweaked slightly, with an addition of ... 2answers 283 views ### Poincaré Section I have encountered somewhat the same problem as here. But with the equations, x'(t) = p(t), p'(t) = - x(t) - y(t), y'(t) = q(t), q'(t) = - y(t) - x(t) My code is, ... 0answers 154 views ### Optimizing a functional using variational calculus Here I am, trying to get the trajectory (x(t),y(t)) that will minimize the following Lagrangian (i.e. the integrand of the functional) between (-1,-1) and (-1,y_{eff}) where x_{eff} is defined ... 2answers 347 views ### Problem with Poincare section these are equations for some double oscillators: x'(t)=p, p'(t)=-x-3y, y'(t)=q, q'(t)=-y-3x I would like to plot the Poincare section for collection of (y,q) when x=0 and x'(t)>0 (or for ... 1answer 164 views ### Simple differential equation to solve Suppose we have this differential equation:$$ x^2 + y^2 + z^2 = \frac{\frac{\partial y}{\partial x}}{x+y+z}$$I want to find \frac{\partial y}{\partial x} at x=1,y=1,z=1. I tried this code but ... 2answers 294 views ### Solve differential equation with 3 variables and plotting contour Suppose we have this equation:$$ 2 - x g(z) f \left(x, \frac{\partial y}{\partial x}\right) = 3y $$using initial condition y = 2 where g = \left| \frac{3}{2-iz} \right| and f = ... 0answers 262 views ### Nonlinear FEM and FindRoot I'm trying to develop a kind of nonlinear FEM application using mathematica to solve a bvp like the following:$$ \gamma(u') ~u^{iv} + 2 \gamma'(u') u''' u''+ u''^3 = f(x) $$where u = ... 2answers 287 views ### Plot integration curve of a system of ODEs I'm really n00b in Mathematica, so please bear with me, as this seems to be my only option to learn how to do what I wany to do. I have a system of two differential equations: ... 3answers 1k views ### Implicitly differentiate an equation, then solve the resulting equation Suppose I have an extremely tedious equation to differentiate and want mathematica to help do the differentiation and solve. Consider a less tedious equation:$$y (x,z) = sin \left(\frac{1}{x} ...
I am trying to solve the following hyperbolic equation with given boundary conditions: I choose as initial condition $u=1$, and evolve the above hyperbolic equation until reaching a stationary ...