非线性刚性微分方程一类新的高效数值方法.pdfVIP

℄℄ B- EBDF ℄ New BDF ÆNBDF k NBDF k B- k k EBDF ℄ k = 2, 3, ..., 8 k EBDF k − 1 B- NBDF EBDF ℄℄ NBDF EBDF B- NBDF  ℄ B- EBDF NBDF I Abstract Based on B-theory of numerical methods for nonlinear stiff differential equations, we modify the existing EBDF methods, and construct a new class of efficient numerical methods which are known as New BDF methods with abbreviation NBDFs. It is proved that the k step NBDF method is B-consistent of order k and convergent of order k in the classical sense, and has the same perfect numerical stability properties as the k-th order EBDF method, where k = 2, 3, , 8. However, the k-th order EBDF method has an essential drawback that it’s B−consistency order is one less than the convergence order. Fortunately, this drawback is overcome by our New BDF methods constructed. Theoretical analysis and numerical experiments show that for solving nonlinear stiff problems the computational accuracy and efficiency of an NBDF method is usually much higher than the corresponding EBDF method of the same order, the latter usually causes order reduction, but the former usually has observed order closely near to its B-consistency order. Therefore, we can conclude that the NBDF methods constructed in the present paper are of importance in practice. Key Words:Nonlinear stiff differetial equations; B-theory; EBDF methods; NBDF methods; accuracy and stability analysis II . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (I) Abstract . . . . . . . . . . . . . . . . . . . . .