A new one-step hybrid block method with third derivatives and optimized features aimed at solving the classical one-dimensional Bratu’s and Reactor design problems is developed. The development of the new method considers three intermediate points that are properly chosen through the optimization of the local truncation errors corresponding to the main formulas to approximate the solution and the first derivative at the end point of the block, and another approximation of the solution at an intermediate point. The convergence analysis and the order of the proposed method are analyzed. Some specific problems are solved to demonstrate the efficiency and feasibility of the technique adopted. The numerical results provided through the implementation of the scheme are very much closer to the exact solutions and are found favorably compared with different methods in the available literature.

开发了一种具有三阶导数和优化特征的新型一步混合块方法，旨在解决经典的一维布拉图和反应堆设计问题。新方法的开发认为是通过对应于主公式来近似在该块的结束点的溶液和一阶导数的局部截断误差的优化适当选择三个中间点，并在该溶液的另一种近似一个中间点。分析了算法的收敛性和排序。解决了一些特定问题，以证明所采用技术的效率和可行性。