Mathematical analysis of the nonlinear systems arising in the industry.

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We have obtained the following results.1. We showed the effectiveness of the multiple precision arithmetic to approximate the solutions of PDE‘s which have transition phase and the blow up in finite time.2. We derived the default risk model equation and analyze theoretically and numerically.3. We showed the existence and the finite dimensional property of the attractors in magnetic Benard problem4. We applied the multi-precision computation to the equation with delay term,which is hard to compute, and showed that in the case the solution is analytic, it is effective.