Solving Ordinary Differential Equations I: Nonstiff Problems

By Ernst Hairer, Syvert P. Nørsett, Gerhard Wanner. 2009

722 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/21a5f22585fbcb9a3d4b0eff83d82ae1d7178fba

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Citations in the corpus

On an accurate third order implicit-explicit Runge--Kutta method for stiff problems (2009, methodology): “Notice that the free parameter c4 has been computed to minimize the fourth-order error terms [15].”
Learning Differential Equations that are Easy to Solve (2020, methodology): “When h is sufﬁciently small, the numerical error of a m th-order method is bounded by ˆz ( t + h ) − z ( t + h ) ≤ ch m +1 for some constant c (Hairer et al., 1993).”
Understanding Machine-learned Density Functionals (2014, unknown): “The ﬁrst is to compute the functional-driven error ∆T F = ˜ T [ n ] − T [ n ], which is simply the error in the KE evaluated on the exact density.”
Applied Stochastic Differential Equations (2019, unknown): “For more details on ODE methods and theory, the reader is referred to the books of Kreyszig (1993), Tenenbaum and Pollard (1985), and Hairer et al. (2008), although the same information can be found in many other books as well.”
Numerical Integration of Ordinary Differential Equations (2009, unknown): “nofailed = true; % no failed attemps while true hA = h * A; hB = h * B; f(:,2) = feval(ode,t+hA(1),y+f*hB(:,1),args:); f(:,3) = feval(ode,t+hA(2),y+f*hB(:,2),args:); f(:,4) = feval(ode,t+hA(3),y+f*hB(:,3),args:); f(:,5) = feval(ode,t+hA(4),y+f*hB(:,4),args:); f(:,6) = feval(ode,t+hA(5),y+f*hB(:,5),a”
Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review (2016, methodology): “Probably the earliest DIRK-type methods, apart from the first-order accurate, Lstable implicit Euler method, are the implicit midpoint and trapezoidal (Lobatto IIIA) rules, both of which are second-order accurate and A-stable [190].”
A new class of energy-preserving numerical integration methods (2008, unknown): “Here we have used the standard representation of elementary differentials by rooted trees [2, 10].”