This article gives a brief introduction of using multiple precision(MP) computing and interval analysis(IA) in the study of science computation. First it reveals the sensitive dependency of floating point computational results on computation precision and step-size and its indeterminacy in the computation of the Lorenz nonlinear equations by applying a MP method, and then studies the method for obtaining a real numerical solution. The paper also discusses a new multiple-precision-based scheme to identify the maximum effective computation time(MECT) and optimal step-size(OS). Moreover, the concept of interval analysis is shown and the application of interval analysis in the proof of the existence of chaotic attractor for Lorenz equation is demonstrated. These advanced numerical computation concepts and tools are valuable for the research of fluid mechanics, atmospheric sciences and nonlinear dynamical systems.