Hybrid Symbolic-Numeric Methodology

Symbolic and numerical computation are traditionally thought of as separate, to the detriment of users. In Mathematica, they are seamlessly integrated, enabling unique hybrid methods for many problems and ensuring consistent results whenever quantities of any precision are combined.

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Solving a second - order differential equation

Step 1: Rewrite the equation manually as an equivalent set of first-order equations

Step 2 : Write an externel file to evaluate the function as a column vector

Step 3 : Set the global variable μ and compute the solution vector

Step 4: Extract the solution for (Subscript[y, 1])

Step 5 : Plot the solution

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Solving a second - order differential equation with Mathematica

Step 1: Enter the differential equation and initial conditions using NDSolve

μ=3.2;
sol = NDSolve[{D[x[t],t,t]+x[t]-μ D[x[t],t](1-((x[t])^2))==0,x[0]==1,x'[0]==0},x,{t,0,30}];

Step 2 : Plot the result

Plot[x[t]/.sol,{t,0,30}]

ADDITIVE GmbH, mathematica@additive-net.de, 06172-5905-30