Questions tagged [differential-equations]

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

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29 views

Using NDSolve and PieceWise for boundary conditions for coupled PDEs

I've decided to try and use PieceWise in my boundary conditions for my 4 coupled PDEs, but it doesn't seem to work out nicely. I'm receiving the error: NDSolve::overdet: There are fewer dependent ...
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1answer
661 views

Differential equation solution

DSolve[y''[x] + (a - (b*x^2 - c)*x^2)*y[x] == 0, y[x], x] I couldn't solve this equation, please help
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44 views

Confluent Heun function

Does this function (confluent Heun function) exist in Mathematica? I try to solve the following equation, ...
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47 views

Hopf bifurcation for competitive system

I am attempting to visually investigate a Hopf bifurcation in the xz plane in a competitive system but have no idea how to input some of these values so I may adjust some of the parameters as ...
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1answer
103 views

Solving and plotting derivative included function

Please suggest a method that I can use to solve (for y(x) and y'(x)) and plot the derivative related given function. Note: L may be vary): ...
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1answer
36 views

Can this PDE be solved through DSolve?

I was trying to solve the linear advection pde, using DSolve. I was able to do it using NDSolve, but I was curious to see if Mathematica was able to give the well-...
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1answer
54 views

Manipulate NDSolve

Can anyone help me? This is my code: f[x_ ] = x Exp[I z]] (Cos[z]] BesselJ[l, a *x] - BesselY[l, a *x] Sin[z]) u=0.1 v=6 on the other hand hand: ...
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3answers
67 views

Plot an Integral of NDSolve solution

I have a problem with plotting the integral of an NDSolve solution. I have attached the code for a simple 2nd order linear ODE to be solved by NDSolve and then to be integrated by NIntegrate. I ...
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44 views

I there any way to DSolve an equation by an estimated method?

I am trying to DSolve this differential equation for A[r] ...
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90 views
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Need help solving ODE with ParametricNDSolveValue solver

I am trying to apply @bbgodfrey method for finding the right initial guess for the following problem but I get an error message and I don't understand where it comes from. I would also like to ...
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51 views

Calculating with deformed Heat equation?

How can I implement the following equation and start computing numerically? The first partial derivative can take fractional numbers.
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1answer
148 views

The NDSolvevalue of MMA can not be used to solve the finite element problems according to the stress boundary conditions

The NDSolvevalue of MMA can well solve the finite element problems according to the displacement boundary conditions ...
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45 views

I can't draw the Plot [closed]

I'm running the below code, but it draws an empty graph, and I don't know how to fix it. ...
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2answers
65 views

Shooting with updating BC's

So I have a 'fairly simple' problem that needs to be 'solved'. I have been able to solve this running 2 loops in Matlab but I am sure Mathematica should be able to handle this. I have the ODE $$F'(x)+\...
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23 views

Clear assigned y'[x] from memory [duplicate]

If I, by mistake, write Mathematica assigns $y'(x)=y(x)/5$ and I don't know how to clear that from memory (I had to restart Mathematica). ...
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67 views

NDSolve issue, potential singularity or stiff system

I have the following parameters, equations, and NDSolve solution set up as such: ...
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27 views

Optimal way to approximate initial condition for PDE?

I have a Fokker-Planck PDE \begin{align} \frac{\partial p}{\partial L}(L,\eta) = \eta^2\frac{\partial^2 p}{\partial\eta^2}(L,\eta) +(1-2\eta)\frac{\partial p}{\partial\eta}(L,\eta)+\frac{2(\eta-1)}{\...
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1answer
596 views

Solving a PDE with its boundary condition expressed as a piecewise function

All I want to do is solve the PDE pde = D[y[x, t], t] + y[x, t] D[y[x, t], x] == 0 with the boundary condition expressed as a piecewise function, say, ...
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1answer
285 views

How to handle this constant-interval integral in ODE?

The problem is to solve a system of nonlinear equations with a definite integral. $Q_i(x), i=1,2,3, x \in [-\text{max},\text{max}]$ \begin{align*} a_iQ_i''(x)-b_i(\vec{Q})-d_i\int_{-\text{max}}^{\text{...
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1answer
43 views

Numerical Issues Using Results of NDSolveValue

I am solving Laplace's Eqn. (Cartesians) in 2D in a region which is infinite in x, semi-infinite in y, and bounded by a function of x (h[x] in my code) close to y=0....
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1answer
74 views

Calculate sensitivities of differential algebraic equation

I would like to calculate sensitivities for a DAE. The DAE can be solved in Mathematica by: ...
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1answer
64 views

How to plot solution of first order time dependent differential equations with other parameter not with time

I am trying to plot the solution given in the code with respect to "delc", not w.r.t time "t". I don't know what to do for getting the plot between solution and value "delc" which vary 0 to 2. The ...
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1answer
350 views

Boundary Problems

I am trying to study what happens to a wave as it passes different boundaries. This is the working wave equation defined on a plane ...
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1answer
39 views

AppendTo inside ParallelMap

I think this question has never been fully answered. In here the problem has already been mentioned, but let me give a MWE. I will solve a given ODE for a wide range of initial conditions and I want ...
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2answers
100 views

NDSolve and Euler method

I would like to solve $y'(x)=x^2-y^2,y(0)=4$ with two ways, NDSolve and Euler method, and with Runge-Kutta maybe. Then, I 'll try to plot all of them in one graph. I had with NDSolve: ...
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1answer
100 views

A system of differential equations [closed]

Consider the following system of differential equations: $$x'(t) = a\, x(t) - b \,x(t) y(t),$$ and $$ y'(t) = c\, x(t) y(t) - d \,y(t),$$ with $$ x(0) = x_0, y(0) = y_0$$ For example, we may have: <...
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54 views

Ground state Of Gross Pitaevskii Equation

I want to plot the ground state of Gross-Pitaevskii equation using NDSolve. I am using the following code: ...
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1answer
82 views

Solving a system of coupled ODEs

I am trying to solve these 9 coupled ODEs ...
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1answer
95 views

Nonlinear differential equation with unknown parameter and integral form boundary condition

I'm trying to solve numerically a non-linear problem in order to determine the velocity field ($U$) and the film thickness ($h$) of a non-Newtonian fluid over an inclined plane. The equations are, $$\...
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28 views

NDSolve error when integrating two second order coupled ODEs

I want to plot a solution for a system of two second order coupled ODEs: ...
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1answer
49 views

Adjusting PrecisionGoal and AccuracyGoal when solving my equation using NDSolve?

Thanks for paying attention to my question and modifying my terrible formatting[facepalm], now I think I've found the answer. The point is the selection ...
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1answer
45 views

Error message when trying to solve 2 coupled PDEs using NDSolve

I'm currently facing a problem when trying to solve 2 coupled PDEs. I get the warning messages: NDSolve::fembdcc: Cross-coupling of dependent variables in DirichletCondition[IPF==IPB/10,z==5.] is not ...
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1answer
63 views

Plotting a two parameter function evaluated at a specific point

I am trying to solve the following problem: given the differential equation $$\frac{d^2y}{dx^2}+\bigg(a+b\frac{2}{\pi}\tan^{-1}x\bigg)y=0$$ subjected to two different initial condition we get two ...
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64 views

DSolve function is not working for Hypergeometric Function

I am trying to get the solution of second order differential equation, but it is not working. Any idea about it will help me a lot. ...
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2answers
817 views

Solving stiff boundary value problem

Im trying to solve a nonlinear ODE with boundary conditions, the simplified problem reads for example $$ k \frac{\mathrm d^2 T}{\mathrm d x^2} = T^4\, , \quad x \in[0,\, 1]\, , \\ T(0)=0.9\,,\quad T(1)...
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1answer
54 views

Maximizing Output from ParametricNDSolve [closed]

Given a system of differential equations that are dependent on two parameters, such as the system below (the equation below is not that important, I am interested in a general procedure given a ...
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1answer
108 views

Why can't MMA solve this system of differential equations?

This system of differential equations can be solved in order to obtain the expression of x[t] y[t] z[t] ...
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0answers
33 views

Unexpected stiff system error [closed]

Let there be the following functions ya[t_, x_] := Cosh[t*x] za[t_, x_] := Sinh[t*x] wa[t_, x_] := x*Sinh[t*x]^2 One can verify that the following PDE's hold <...
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Heat transport with Neumann bc in older Mathematica versions [duplicate]

Im trying to solve a simple heat transfer equation: $\partial_t T-\beta \partial_{xx}T=0$ for a finite system $x\epsilon <0;L>$ along with initial/boundary conditions: 1) $T(x,t)=0$ for $t<...
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1answer
67 views

“Fewer dependent variables than equations, so the system is overdetermined” without any BC's

Consider this system of PDEs. eqn1 = D[u[x, t], x] + 5 D[u[x, t], x, x] + D[v[t], t, t] - 4 == 0 eqn2 = D[v[t], t] + D[u[x, t], t, t] + v[t] == 0 I would like to ...
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1answer
99 views

Solving Laplace's equation in 2D using region primitives

I was looking at examples of solving problems in electromagnetism and ran across this question, which was a great example of just that. However, looking at the Dirichlet condition, both answers define ...
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67 views

A system of linear differential equations with variable (time-dependent) coefficients

I have searched almost all similar pages discussing a system of differential equations, but none of them discussed the case of variable coefficients. My problem is a bit more complicated, because ...
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1answer
41 views

NDSolve with Events that reevaluate with different Discrete Variables

I have the following problem: I have a set of ODEs and some discrete variables which I can solve successfully. Now I want mathematica to check at every $0.1 \,t$ time step, wether it would increase ...
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0answers
78 views

find ODE solutions and suitable initial conditions to get solution

DSolve[2.56 x''[t] == -0.32 x'[t] - x[t] - 0.05 x[t]^3 + 2.5 Sin[t], x[t], t] I want to find the solution and find two initial conditions such that their ...
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2answers
80 views

Manipulate NDsolve 1D-reaction diffusion equation

I want to solve the following 1D-reaction diffusion equation: $$\frac{\partial}{\partial t}u(t,x)=\alpha\,\frac{\partial^{2}}{\partial x^{2}}u(t,x)+a\,u(t,x)$$ $$u(t,0)=0\,\,\,\,\,\text{et}\,\,\,\,\,u(...
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1answer
96 views

Solving Piecewise Differential Equation using NDSolve (coupling at BC)

I am having some issues in dealing with a system of differential equations. I would like to solve a 1D diffusive heat equation across several regions with different material properties. I now have a ...
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0answers
64 views

Fit a three-pulse sequence

I am wondering how to properly fit the three-pulse sequence shown below. I have tried a method which is fitting the three pulses with three polynominal functions seperately and then finding the x-...
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1answer
129 views

How to create an animation of charged particles' motion in an electric field

I am trying to create an animation of 3 particles' motion in an electric field. The electric field is created by a needle attached to a top plate both of which are at -3800V with a grounded plate ...
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1answer
68 views

solving coupled differential equations

I am solving 6 differential equations in matrix form as: ...