A functional fitting Runge-Kutta method with variable coefficients

D.G. Bettis, Numerical integration of products of Fourier and ordinary polynomials. Numer. Math.,14 (1970), 424–434.

J. Butcher, The Numerical Analysis of Ordinary Differential Equations. Wiley, 1987.

J.P. Coleman, P-stability and exponential-fitting methods fory″ = f(x, y). IMA J. Numer. Anal.,16 (1996), 179–199.

W. Gautschi, Numerical integration of ordinary differential equations based on trigonometric polynomials. Numer. Math.,3 (1961), 381–397.

E. Hairer and G. Wanner, Solving Ordinary Differential Equations II (2nd edition). Springer, 1996.

T.E. Hull, W.H. Enright, B.M. Fellen, and A.E. Sedgwick, Comparing numerical methods for ordinary differential equations. SIAM J. Numer. Anal.,9 (1972), 603–637.

A. Iserles, A First Course in the Numerical Analysis of Differential Equations. Cambridge, 1996.

M. Nakashima, Variable coefficient A-stable explicit Runge-Kutta methods. Japan J. Indust. Appl. Math.,12 (1995), 285–308.

K. Ozawa, A four-stage implicit Runge-Kutta-Nyström method with variable coefficients for solving periodic initial value problems. Japan J. Indust. Appl. Math.,16 (1999), 25–46.

F.L. Shampine, Numerical Solution of Ordinary Differential Equations. Chapman & Hall, 1994.

T.E. Simos, Some new four-step exponential-fitting methods for the numerical solution of the radial Schrödinger equation. IMA J. Numer. Anal.,11 (1991), 347–356.

R.M. Thomas, T.E. Simos and G.V. Mitsou, A family of Numerov type exponential fitted predictor-corrector methods for the numerical integration of the radial Schrödinger equation. J. Comput. Appl. Math.,67 (1996), 255–270.

J. Vanthournout, G. Vanden Berghe and H. De Meyer, Families of backward differentiation methods based on a new type of mixed interpolation. Comput. Math. Appl.,20 (1990), 19–30.