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

learn more… | top users | synonyms

0
votes
0answers
2 views

NDSolve::derarg error: requiring pure function in solving differential equations

I'm trying to numerically solve 2 partial differential equations eq1 and eq2 given the boundary conditions in cond1 using the following code ...
1
vote
1answer
63 views

How to tell NDSolve about known relations of the exact solution

The solution to this system of differential equations: ...
0
votes
0answers
33 views

Customizing display of partial differential equations

I am manipulating partial differential equations symbolically, and would like to get the easily readable form $\rho \frac{\partial v}{\partial t}$, leaving variables implicit. Based on suggestions ...
0
votes
0answers
15 views

How can I calculate matrix differentiation? [on hold]

I am studying about the Matrix Differentiation. I don't know if this red box differential metric, which is how it is calculated.
1
vote
1answer
87 views

Need help solving a system of two 1st order nonlinear differential equations

The original system of equations reads: $\begin{cases} f'(r) + f(r) \left(a(r) - \frac{1}{r}\right) = 0,\\ f^2(r) + a'(r) + \frac{a(r)}{r} - 1 = 0\,, \end{cases}$ with boundary conditions $f(0) = ...
0
votes
0answers
37 views

DSolve solves PDE only without boundary condition, but fails otherwise

I'm trying to solve for Te[w, Pprobe, t] in a partial differential equation. What's surprising is that it manages to solve it when I don't put in any initial ...
0
votes
1answer
48 views

How to find the value of a solution of an ODE at a particular point [on hold]

I'm trying to find the value of $z(y)$ at a particular time, say $y=0.5$. I've solved the differential equation. I tried using z3 = z[3] /. sol, but it's not ...
2
votes
0answers
44 views

EquationTrekker-like behavior for state space?

EquationTrekker is great for phase space plots, however I want to plot the results of $$\phi '(t)=-b \sin (\phi (t))+g \sin (\Phi (t)-\phi (t))+1\\\Phi '(t)=g y ...
3
votes
1answer
133 views

Issue in ParallelTable after evaluating another function using NDSolve and FindRoot. What is wrong with this inverse?

I am trying to find the inverse of a function which is defined through NDSolve and NIntegrate. The question is pretty similar ...
3
votes
1answer
86 views

Already solved DE, now I need to rearrange and plot

I have solved for $z(w,x,y)$ in a differential equation: $$ 3\frac{\partial z}{\partial y} = 2(z-1) + (1-wy^2 )x $$ And I obtained the general solution: $z = f(w,x,y)$ Now putting in $x=0$, we have ...
1
vote
1answer
41 views

Solved the differential equation, how to rearrange to find solution? [closed]

I have solved for values of $y(x)$ from $1 < x < 2$ and plotted them: ...
-1
votes
0answers
68 views

Can Mathematica solve my system of differential equations? [closed]

I have a system of differential equations about two unknown functions $f(x)$ and $g(x)$: $$\phi_1(x)=\alpha_1 g(x) \frac{d}{dx}f\left(x+\frac{g(x)}{g'(x)}\right)$$ $$\phi_2(x)=\alpha_2 [1-f(x)] ...
0
votes
2answers
65 views

Solve simple differential equation - Error?

I get the error "The function Te appears with no arguments." when running this code. I'm not sure why. Is it because of the $Abs[\Gamma]$ ? ...
2
votes
1answer
139 views

how to solve ODE with boundary at infinity

y''[x]-x y[x]==0 y[0]==AiryAi[0], y[infinity]==0 the analytic solution to this ODE is the Airy function y[x]=AiryAi[x] if I ...
0
votes
2answers
152 views

Plotting a solution of the Allee Effect

I am doing a project on the Allee Effect. I am able to successfully create a stability analysis. That is, I can find the relevant equilibrium points ($y_e = 0,\ y_e = \alpha$ and $y_e=k$) and draw ...
0
votes
1answer
97 views

DSolve problem with system of linear ODEs

I encounter a rather strange problem in Mathematica when trying to solve the following system of linear differential equations: ...
1
vote
0answers
140 views

Problem with NDSolve in Mathematica 9 / 10

I'm having trouble by solving the following differential equation in Mathematica 9 and 10, where the code works fine in version 7: ...
1
vote
1answer
87 views

Using spherical derivatives with NDSolve

I am trying to plot the path of an object around a centre of mass. Obviously this needs spherical coordinates. The problem I encounter is with the derivatives. The Derivatives in spherical coordinates ...
5
votes
2answers
73 views

Automatically detect largest interval over which NDSolve can find a solution

Question: Consider the following numerical resolution: NDSolve[eqn, {x1[t], x2[t], y[t]}, {t, tmin, tmax} where eqn, ...
3
votes
1answer
96 views

Is it possible to obtain explicit symbolic solutions to such linear ordinary differential equations?

The ordinary differential equations to solve have symbolic parameters $k_1,k_2,k_3,k_4,k_5,k_6 \in \mathbb{R}$. $$ \left\{ \begin{array}{l} {y_1}'(t)=-{k_1} {y_1}(t)-{k_2} {y_1}(t),\\ {y_2}'(t)={k_2} ...
1
vote
1answer
168 views

Solving a nonlinear PDE with Mathematica10 FEM Solver

I am trying to solve a system of coupled nonlinear PDEs in a rectangular region with the new FEM solver in Mathematica 10. However, I come across an error stating NDSolveValue::femnonlinear: ...
1
vote
1answer
103 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: ...
2
votes
1answer
160 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 ...
1
vote
1answer
34 views

WhenEvent “StopIntegration” problem

The first example on the WhenEvent help page is ...
0
votes
0answers
36 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 ...
0
votes
1answer
59 views

Solution of a set of ODEs

How can I write code to solve a set of ODEs in two-coordimate (i,j) system? Example: ...
1
vote
0answers
102 views

Use Runga-Kutta method to solve a system of many ODEs [closed]

For my simulation purpose, I need to solve the following system of DEs using 4th-order Runga-Kutta (RK) method in Mathematica: $$ I_{k,0}'(t) = -\beta_1~I_{k,0}(t) + k~\lambda~ \Theta(t) + \gamma~ ...
1
vote
2answers
224 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 ...
2
votes
0answers
84 views

Edge finite elements in Mathematica [closed]

I am wondering if it's possible to extend the Finite Element capabilities of Mathematica so as to include other types of elements such as edge vector elements (Nedelec) which can be used in ...
1
vote
2answers
72 views
1
vote
0answers
24 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 ...
34
votes
2answers
1k 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 ...
0
votes
0answers
30 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, ...
-1
votes
1answer
45 views

NDSolve solution methods issue

I´m modelling a biological reaction thorugh a set of differential equations. ...
4
votes
2answers
127 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: ...
5
votes
3answers
149 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: ...
6
votes
0answers
103 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 ...
2
votes
1answer
51 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 ...
0
votes
0answers
38 views

Complex infinities in an Euler-Lagrange equation

I now wish to solve for $L(t)$ and $H(t)$ some ugly Lagrangian (in the code below) in configuration space, respectively the length and the height of a system. I tried running the code below, with the ...
4
votes
1answer
109 views

1/0 encountered when solving an ODE

What can cause this error to show up? Clear[lambda, a, b, x, y]; ode = lambda y[x] + a b y'[x] + a (-1 + b x) y''[x] + y''''[x] == 0; DSolve[ode, y[x], x] ...
0
votes
0answers
66 views

Plotting Geodesics in Kerr

I'm interested in plotting the trajectories of null geodesics near a rotating black hole (given by the Kerr solution) which involves a system of first order differential equations. Some Context (not ...
3
votes
0answers
52 views

Error solving third order ODE in version 10. No error in V9. DSolve`DSolveKovacicDump`

This is an ode which is solved with no error in V9, but gives a very strange error in V10. Is this a regression bug? On version 9, the ode is solved with no error ...
24
votes
3answers
802 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 ...
2
votes
0answers
42 views

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

I encountered this when trying to solve this problem with DSolve: ...
1
vote
1answer
84 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 ...
0
votes
0answers
56 views

Trouble outputting Plot

I am trying to solve a system of ODEs and plot them with Manipulate but I keep getting blank outputs. Below is my code: ...
1
vote
0answers
45 views

solution of differential equation with complex roots

How to find the solution of differential equation with complex roots For example of [{y^2 n[t]+ 2 k y n'[t] + n''[t]= M p sin(o t), n[0]==0, n'[0]==0}, n,t] given k lies between 0 to 1 which makes the ...
8
votes
3answers
190 views

Should DSolve always return solution with constant of integration?

Version 10.0 Clear[y,x]; DSolve[D[y[x], x] - y[x]^2 + y[x]*Sin[x] - Cos[x] == 0, y[x], x, GeneratedParameters -> C] or ...
3
votes
1answer
73 views

Factoring a differential equation into an operator product

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} ...
1
vote
0answers
72 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, ...