Thesis Open Access
NUMERICAL SOLUTION OF INITIAL VALUE PROBLEM OF BRATU TYPE EQUATIONS USING EIGHTH ORDER PREDICTOR-CORRECTOR METHOD
ABOMA TAMANA GAMACHU
ABSTRACT The primary purpose of this research was to construct an eighth-order predictor–corrector numerical scheme for solving second-order initial value problems associated with Bratu-type differential equations. The developed method is examined through stability and convergence analysis in order to evaluate its theoretical reliability. Numerical experiments are conducted to test the effectiveness and computational performance of the proposed approach. The approximate numerical results are compared with the corresponding exact solutions to determine the accuracy of the method. The comparison indicates that the proposed scheme produces highly accurate results with very small absolute errors. Furthermore, the influence of different step sizes on the accuracy of the numerical solutions is investigated. The study also demonstrated that smaller mesh sizes improve the precision of the obtained solutions. Several model examples are provided to verify the applicability, efficiency, and robustness of the developed predictor–corrector method.
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- Publication date:
- July 17, 2026
- DOI:
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- Communities:
- License (for files):
- Statistics Canada: Data Liberation Initiative (DLI) - Model Data Use Licence