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Numerical integration of stiff problems using a new time-efficient hybrid block solver based on collocation and interpolation techniques

Author

Listed:
  • Qureshi, Sania
  • Ramos, Higinio
  • Soomro, Amanullah
  • Akinfenwa, Olusheye Aremu
  • Akanbi, Moses Adebowale

Abstract

In this study, an optimal L-stable time-efficient hybrid block method with a relative measure of stability is developed for solving stiff systems in ordinary differential equations. The derivation resorts to interpolation and collocation techniques over a single step with two intermediate points, resulting in an efficient one-step method. The optimization of the two off-grid points is achieved by means of the local truncation error (LTE) of the main formula. The theoretical analysis shows that the method is consistent, zero-stable, seventh-order convergent for the main formula, and L-stable. The highly stiff systems solved with the proposed and other algorithms (even of higher-order than the proposed one) proved the efficiency of the former in the context of several types of errors, precision factors, and computational time.

Suggested Citation

  • Qureshi, Sania & Ramos, Higinio & Soomro, Amanullah & Akinfenwa, Olusheye Aremu & Akanbi, Moses Adebowale, 2024. "Numerical integration of stiff problems using a new time-efficient hybrid block solver based on collocation and interpolation techniques," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 220(C), pages 237-252.
    • Handle: RePEc:eee:matcom:v:220:y:2024:i:c:p:237-252
    DOI: 10.1016/j.matcom.2024.01.001
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