Computation Sequences for Series and Polynomials

摘要: Approximation to the solutions of non-linear differential systems is very useful when exact are unattainable. Perturbation expansion replaces system with a sequences smaller problems, only first which typically linear. This works well by hand for few terms, but higher order computations too demanding all most persistent. Symbolic computation thus attractive; however, symbolic expansions almost always encounters intermediate expression swell, we mean exponential growth in subexpression size or repetitions. A successful management spatial complexity vital compute meaningful results. thesis contains two parts. In part, investigate heat transfer problem where two-dimensional buoyancy-induced flow between concentric cylinders studied. Series respect Rayleigh number used an approximation solution, using symbolicnumeric algorithm. Computation help reduce expressions. Up 30 computed. Accuracy, validity and stability computed series solution second Hilbert’s 16 investigated find maximum limit cycles certain systems. Focus values perturbation theory, form multivariate polynomial The real roots such leads possible cycle conditions. modular regular chains approach triangularize roots. 9 constructed