![]() ![]() ![]() the boundary value problem is reduced to two initial value. Well, personally I feel the behavior of ParametricNDSolveValue undesirable, why it doesn't return a List of ParametricFunction?įinally, my intuition told me that you may be interested in this post. Program (Linear Shooting method): to approximate the solution of the boundary value problem x ( t) p ( t) x ( t) + q ( t) x ( t) + r ( t) with x ( a) and x ( b) over the interval a,b by using the Runge-Kutta method of order 4. You'll still see some warnings when you execute the above code, but it's mainly because of the nature of your equation and it's another issue, at least FindRoot works this time! As you begin to understand your system more deeply, you will find ways to simplify it. What I want to find is the maximum radius (r) when ϕ = 0, ϕ' = 0, A = 0, A' = 0.ī = ParametricNDSolveValue Popular answers (1) George Mengov Sofia University 'St. The boundary conditions of these equations are ϕ = 1, ϕ' = 0, A = 0, A' = 0īecause of the singularity of r, we assume r = 1*10^-8. Where mb, mv and g are constants equal to 1. Any solution to this problem would be of interest.I have 2 coupled differential equations with an eigenvalue Ei and want to solve them ϕ'' + (2/r) ϕ' - mb^2 ϕ + (Ei + g*A)^2 ϕ = 0Ī'' + (2/r) A' - mv^2 A - 2 g (Ei + g*A) (ϕ)^2 = 0 We present algorithms to solve coupled systems of linear differential equations, arising in the calculation of massive Feynman diagrams with local. The solving of a simple independent differential equation is very easy but the difficulty comes when equations are coupled. ![]() So, I was wondering if someone could help me how to solve this analytically. There is a free version of Mathematica featuring its syntax and functions- Mathics that was developed by a team led by Jan Pschko. This computer algebra system has tremendous plotting capabilities. Of course, I could get the numeric solution, but I could not get the same result obtained from Eq. Mathematica provides friendly tools to solve and plot solutions to differential equations, but it is certainly not a panacea of all problems. I have been trying for two weeks now, but could not figure out the solution. Also, ode15s and ode23tb are good options ,in case, ode45 does not work. At first I tried to solve it using just the BVPs but Mathematica couldnt do it, so I started using shooting method and turning it into an IVP. You can adopt MATLAB - ode 45 (R K Method of fourth order) for non-linear coupled equations. Making statements based on opinion back them up with references or personal experience. Provide details and share your research But avoid Asking for help, clarification, or responding to other answers. If f 3 ( x) 0, then the Abel equation reduces to either Bernoulli equation or to Riccati equation. Thanks for contributing an answer to Mathematica Stack Exchange Please be sure to answer the question. DSolveValue takes a differential equation and returns the general solution: (C1 stands for a constant of integration.) In 1. I won't give the exact problem, but the following is something analogous: The equations. The Wolfram Language can find solutions to ordinary, partial and delay differential equations (ODEs, PDEs and DDEs). Although solving this sort of equation with two masses, no damping (dissipation) and with only one driving force is simple enough, even by hand, it is impossible to do the same for a system with two different damping constants and two driving forces. Im trying to solve these two coupled 2nd order differential equations: with the following boundary conditions. An Abel equation of the first kind, named after Niels Abel, is any ordinary differential equation that is cubic in the unknown function: y f 3 ( x) y 3 + f 2 ( x) y 2 + f 1 ( x) y + f 0 ( x), where f 3 ( x) 0. I am not sure how to plot and solve them using Mathematica. I just do not know how.Īttached is the system I am trying to solve. ![]() However, I have found in many papers and books writing out analytical formula of the solutions to such coupled equations. I have posted a similar question in another forum where the general consensus seems to suggest that it is not possible to symbolic solve a system of coupled second order differential equations with damping (dissipation) and driving forces. ![]()
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