References

A NEW FORMULAE OF VARIABLE STEP 3-POINT BLOCK BDF METHOD FOR SOLVING STIFF ODES


[1] K. H. K. Anuar, K. I. Othman, F. Ishak, Z. B. Ibrahim and Z. Majid, Developing partitioning intervalwise block method for solving ordinary differential equations, In Proceeding of the World Academy of Science, Engineering and Technology (2011), 243-245.

[2] J. Cash, On the integration of stiff systems of ODEs using extended backward differentiation formulae, Numerical Mathematik 34(3) (1980), 235-246.

[3] C. F. Curtiss and J. O. Hirshfelder, Integration of stiff equations, In Proceeding of the National Academy of Sciences of the United States of America (1952), 235-243.

[4] G. Dahlquist, A special stability problem for linear multistep methods, BIT Numerical Mathematics 3(1) (1963), 27-43.

[5] S. O. Fatunla, Block methods for second order ODEs, Intern. J. Computer Math. 41 (1991), 55-63.

[6] C. W. Gear, Numerical initial value problems in ordinary differential equations, COMM. ACM 14 (1971), 185-190.

[7] Z. B. Ibrahim, Block Multistep Methods for Solving Ordinary Differential Equations, PhD Thesis, Universiti Putra Malaysia, 2006.

[8] Z. B. Ibrahim, K. I. Othman and M. B. Suleiman, Fixed coefficients block backward differentiation formulas for the numerical solution of stiff ordinary differential equations, European Journal of Scientific Research 21(3) 2008), 508-520.

[9] J. Lambert, Computational Methods in Ordinary Differential Equations, John Wiley and Sons, Inc., New York, 1973.

[10] W. E. Milne, Numerical Solution of Differential Equations, John Wiley, New York, 1953.

[11] H. Musa, M. B. Suleiman, F. Ismail, N. Senu and Z. B. Ibrahim, An accurate block solver for stiff initial value problems, ISRN Applied Mathematics (2013).

[12] J. B. Rosser, A Runge-Kutta for all seasons, SIAM Review 9(3) (1967), 417-452.

[13] L. F. Shampine and H. A. Watts, Block implicit one-step methods, Mathematics of Computation 23 (1969), 731-740.

[14] M. B. Suleiman, H. Musa, F. Ismail and N. Senu, A new variable step size block backward differentiation formula for solving stiff IVPs, International Journal of Computer Mathematics (2013).

[15] L. F. Shampine and M. K. Reichelt, The MATLAB ODE suite, SIAM Journal of Scientific Computing 18 (1997), 1-22.

[16] H. A. Watts and L. F. Shampine, A-stable block implicit one-step methods, BIT 12 (1972), 252-266.

[17] J. Williams and F. deHoog, A class of a-stable advanced multistep methods, Mathematics of Computation 28 (1974), 163-177.

[18] S. A. M. Yatim, Z. B. Ibrahim, K. I. Othman and M. B. Suleiman, A quantitative comparison of numerical method for solving stiff ordinary differential equations, Mathematical Problems in Engineering (2011), 1-12; Article ID 193691.