Tagged Questions

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

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NDSolve divide-by-zero trouble

So I have a set of differential equations (which I know are analytically integrable) but I want to integrate them numerically to get the form of the solution (the solution is not explicit and hence I ...
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Numerical solution of Bessel-like equation using NDSolve

I need to calculate solution of Bessel-like equation having general form: $\frac{d^2F}{dr^2}+\frac{1}{r}\frac{dF}{dr}+Q(r)F(r)=0$. Problems come from the points near $r=0$ leading to numeric errors. ...
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NDSolve giving the wrong solution?

I'm considering the non-linear second order ODE DE $=0$, with DE given by ...
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Speeding up WhenEvent + NDSolve (Performance tuning and handling instabilities)

I am solving a non-linear partial differential equation using NDSolve. The equation models a liquid film on an isothermal solid substrate. As a result of various fluid physics mechanisms such as ...
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Evaluating solution from NDSolve at a specific point

sol = NDSolve[{eq, iv}, {f[x, t]}, {x, 0, 1}, {t, 0, 10}]; sol[0,1] I want to evaluate the solution from NDSolve at any given point, but when I do the above, ...
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system of differential equations 3 DSolve [closed]

dS/dt = a - dS - λ S I + β R dI/dt = λ S I - (d + m)I dR/dt = m I- (d + β)R Solve the above equation and plot the curve.
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Difference between using NIntegrate and Integrate inside NDSolve?

The differential equation I am considering depends on an integral, which I would like to solve with NIntegrate (since it will gets more complicated and thus I have to use NIntegrate later). My code ...
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DSolve non linear DE

probably my problem i´m gonna ask seems ridiculous and quite basic. I want to solve an equation with the following code, where a,b,c are parameters. But surprisingly they don´t appear in the solution. ...
57 views

Two questions about “wraparound” with “Event” method

I am learning EventLocator method from the document center. As for the following code (copy from this document) solving the sine-Gordon equation, it uses the ...
379 views

ParametricNDSolve KKT Constraint Directly

I am trying to directly solve for an optimal control using Pontryagin Maximum, where H is the Hamiltonian, in the presence of a KKT constraint. The constraint is ignored. I am wondering if a direct ...
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Any possible to save a 'partial' result of NDSolve when it was aborted due to insufficient memory?

I have run a NDSolve code for an extremely long time. Unfortunately, it was aborted because there was insufficient memory available to complete the computation. At ...
116 views

Plotting Limit Cycle

I have Lotka Volterra Equations where the prey equation is modified. The Equations are x'[t]=a*x[t]*(1-x[t]/k)-b*x[t]*y[t] y'[t]=-c*y[t]+d*x[t]*y[t] To plot the ...
106 views

Fitting Three-Dimensional Data with Parameters

I have been trying to fit a model of rate equations to data of three dimensions. The rate equations in my model are as follows. ...
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Numerical fitting trajectory to model that has NDSolve

I have a model which describes the motion of an object on a plane. ...
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Double Integral with NDSolve!

I have fivefold multiple integral and I wanted a speed calculations.I came across on this Question and had already begun the problems. Here is a toy example with simple double integral: ...
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In NDSolve, how to involve in the odes a integration function that depends on ode functions and can't be analytically integrated?

I think it would be better to use this simple code to explain my questions: ...
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Working with Real/Imaginary/Modulus parts of an complex Interpolating Function?

From solving n times a numerical (complex) equation, like: ...
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NDSolve for axisymmetric problem

I would like to solve an axisymmetric Poisson equation on a disk with FEM. The code for Cartesian coordinates works fine: ...
83 views

Solving Differential Equation for derivative

I am new to mathematica and am trying to solve a differential equation. Actually, I am not entirely sure if the system can be called differential equation. I am interested in finding out the second ...
56 views

Writing PDE boundary conditions with derivatives, More general than Neumann

I am solving 2D Laplace equations on f[x,y] with boundary conditions SomeVector[x,y].Grad[f] == 0 This is more general than Neumann. Is there a way to set such boundary conditions for a curved ...
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solving coupled differential equations with parameters subject to optimization problem

I have an equation, but I don’t know how to program it in Mathematica: x[0]==1; y[0]==1; x'[t]==(a+b) x[t] y[t]; y'[t]==a b y[t]/x[t]; where ...