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Zero Stability
Zero-stability, also known as D-stability in honor of Germund Dahlquist Germund Dahlquist (16 January 1925 – 8 February 2005) was a Swedish mathematician known primarily for his early contributions to the theory of numerical analysis as applied to differential equations. Dahlquist began to study mathematics at Sto ..., refers to the stability of a numerical scheme applied to the simple initial value problem y'(x) = 0. A linear multistep method is ''zero-stable'' if all roots of the characteristic equation that arises on applying the method to y'(x) = 0 have magnitude less than or equal to unity, and that all roots with unit magnitude are simple. This is called the ''root condition'' and means that the parasitic solutions of the recurrence relation will not grow exponentially. Example The following third-order method has the highest order possible for any explicit two-step method for solving y'(x) = f(x): y_ + 4 y_ - 5y_n = h(4f_ + 2 f_n). If f(x)=0 identically, this gi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Germund Dahlquist
Germund Dahlquist (16 January 1925 – 8 February 2005) was a Swedish mathematician known primarily for his early contributions to the theory of numerical analysis as applied to differential equations. Dahlquist began to study mathematics at Stockholm University in 1942 at the age of 17, where he cites the Danish mathematician Harald Bohr (who was living in exile after the occupation of Denmark during World War II) as a profound influence. He received the degree of licentiat from Stockholm University in 1949, before taking a break from his studies to work at the Swedish Board of Computer Machinery (Matematikmaskinnämnden), working on (among other things) the early computer BESK, Sweden's first. During this time, he also worked with Carl-Gustaf Rossby on early numerical weather forecasts. Dahlquist returned to Stockholm University to complete his Ph.D., ''Stability and Error Bounds in the Numerical Solution of Ordinary Differential Equations'', which he defended in 1958, with Fr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |