Block backward differentiation formula with off-step points for solving first order stiff ordinary differential equations - Mohd Nasarudin, Amiratul Ashikin (2020)
This thesis compiles four new numerical methods that are successfully derived and presented based on Block Backward Differentiation Formulas (BBDFs) for the numerical solution of stiff Ordinary Differential Equations (ODEs). The first method is a one-point block order three BDF with one off-step point. The second method is developed by increasing the order of one-point block BDF with one off-step point to order four in order to increase the accuracy of the approximate solution. The third and fourth method are extension of the one-point block to two-point block BDFs method with off-step points. The order and error constant of the methods are determined. Conditions for convergence and stability properties for all newly developed methods are discussed and verified so that the derived methods are suitable for solving stiff ODEs. Comparisons of stability regions are also investigated with the existing methods. Newton’s iteration method is implemented in all developed methods. Numerical results are presented to verify the accuracy of the block BDF with off-step points for solving stiff ODEs and compared to the existing related methods of similar properties. The final part of the thesis is by applying the formulated methods in solving the global warming problem and home heating problem as the example that the derived method can be applied to solve a real life application. In conclusion, by adding offstep point, the accuracy is improved. Therefore, it can be an alternative solver for solving first order stiff ODEs.