Abstract
A hybrid second derivative three-step method of order 7 is proposed for solving first order stiff differential equations. The complementary and main methods are generated from a single continuous scheme through interpolation and collocation procedures. The continuous scheme makes it easy to interpolate at off-grid and grid points. The consistency, stability, and convergence properties of the block formula are presented. The hybrid second derivative block backward differentiation formula is concurrently applied to the first order stiff systems to generate the numerical solution that do not coincide in time over a given interval. The numerical results show that the new method compares favorably with some known methods in the literature.
Highlights
The numerical solutions of stiff systems have been one of the major worries for numerical analysts
A numerical method that is potentially good for solving systems of stiff ODEs must have some reliablity in terms of its region of absolute stability and good accuracy
The interval of stability read from the plot of the region of absolute stability gives [−3.4,0]
Summary
The numerical solutions of stiff systems have been one of the major worries for numerical analysts. A numerical method that is potentially good for solving systems of stiff ODEs must have some reliablity in terms of its region of absolute stability and good accuracy The local truncation error of each of the additional formulas of HBSDBDF is obtained.
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