How to write the following nonlinear ODE as a linear ODE by quasilinearization technique?
y''(x)=y^3(x)-y(x)y'(x), 1 less than x less than 2 y(1)=1/2, y(2)=1/3?
Herbert H H Homeier
A general approach to quasilinearization of nonlinear ODEs is described in the article linked below.
http://arxiv.org/pdf/physics/0102041
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R. C. Mittal
y''(x)=y^3(x)-y(x)y'(x) .Replace y3(n+1) = y3(n) + 3y2(n)(y(n+1) - y(n)) = 3y2(n)y(n+1) - 2y3(n) and replace y(n+1)y'(n+1) = y(n)y'(n) + (y(n+1)-y(n))y'(n) + (y'(n+1) - y'(n))y(n)
= y(n+1)y'(n) + y'(n+1)y(n) -y'(n)y(n).
Here n indicates iteration where assume y(0) = (2-x)/2 +(x-1)/3
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Leila Bouzid
A general approach to the quasilinearization technique of nonlinear ODEs is described in the article linked below.
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