### SOLUTION OF SINGULAR RICCATI DIFFERENTIAL EQUATIONS USING THE REPRODUCING KERNEL HILBERT SPACE METHOD

#### Abstract

This paper deals with the approximation the solution of singular Riccati differential equations using the reproducing kernel Hilbert space scheme. The exact solution *u*(*r*) is represented in the form of series in the space . In the mean time, the *n*-term approximate solution *u*(*r*) obtained and is proved to converge to the exact solution *u*(*r*). Some numerical examples have also been studied to demonstrate the accuracy of the present method. Numerical experiments are performed to confirm our theoretic findings.

**2010 Mathematics Subject Classification:** 34*K*28; 34*K*07; 34*B*10

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