An eighth order Backward Differentiation Formula with Continuous Coefficients for Stiff Ordinary Differential Equations

A block backward differentiation formula of uniform order eight is proposed for solving first order stiff initial value problems (IVPs). The conventional 8-step Backward Differentiation Formula (BDF) and additional methods are obtained from the same continuous scheme and assembled into a block matrix equation which is applied to provide the solutions of IVPs on non-overlapping intervals. The stability analysis of the method indicates that the method is L0-stable. Numerical results obtained using the proposed new block form show that it is attractive for solutions of stiff problems and compares favourably with existing ones.

Authors:

• Olusheye Akinfenwa
• Samuel Jator
• Nianmin Yoa

Keywords:

• Stiff IVPs
• System of ODEs
• Backward differentiationformulas
• Block methods
• Stability.

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