Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
A first course in the numerical analysis of differential equations
A first course in the numerical analysis of differential equations
Efficient algorithms for computing a strong rank-revealing QR factorization
SIAM Journal on Scientific Computing
Matrix computations (3rd ed.)
Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations
Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations
Numerical Methods
On the Compression of Low Rank Matrices
SIAM Journal on Scientific Computing
Explicit Exponential Runge-Kutta Methods for Semilinear Parabolic Problems
SIAM Journal on Numerical Analysis
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Accelerating the convergence of spectral deferred correction methods
Journal of Computational Physics
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We introduce a new class of predictor-corrector schemes for the numerical solution of the Cauchy problem for non-stiff ordinary differential equations (ODEs), obtained via the decomposition of the solutions into combinations of appropriately chosen exponentials; historically, such techniques have been known as exponentially fitted methods. The proposed algorithms differ from the classical ones both in the selection of exponentials and in the design of the quadrature formulae used by the predictor-corrector process. The resulting schemes have the advantage of significantly faster convergence, given fixed lengths of predictor and corrector vectors. The performance of the approach is illustrated via a number of numerical examples.