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Approximate Solutions to Ordinary Differential Equations Using Least Squares Support Vector Machines

IEEE Transactions on Neural Networks and Learning Systems, 2012
Siamak Mehrkanoon   +2 more
exaly  

A theorem on the existence of solutions for singular linear systems of ordinary differential equations

The following problem is considered: \[ (1)\quad A(t)\dot x(t)=B(t)x(t)+F(t),\quad t_ 0\leq t\leq t_ 1;\quad(2)\quad x(t_ 0)=x_ 0. \] Here A(t), B(t) are \(n\times n\) matrices, rank \(\{A(t)\}=k=const\). for \(t\in [t_ 0,t,_ 1]\), F(t) is a known n- dimensional vector function, x(t) is the sought n-vector function and \(x_ 0\) is a given n-dimensional
openaire   +2 more sources

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