AN IMPROVED FAMILY OF BLOCK METHODS BASED ON THE EXTENDED TRAPEZOIDAL RULE OF SECOND KIND AND THEIR APPLICATIONS (FULafia Journal of Science and Technology, 2023)
We present a family of three and five step extended trapezoidal rule of second kind (ETR2s) in block form for thesolution of stiff ordinary differential equations. The block methods were derived via interpolation and collocation procedures. We determined the order, error constant, zero stability to show convergence. The absolute stability region of our block methodsindicates that they are A-Stable, hence suitable for stiff system of ODE problems. The solution curves obtained tends to suggest that our methods compete favorably with the well-known ODE Solver ODE23s. Four numerical examples were used to demonstrate the efficiency of the new block methods,the absolute errors attest to the performance of our methods in-terms of accuracy
Keywords: Stiff Ordinary Differential Equations; Extended Trapezoidal Rule; General Linear Methods; Matrix Finite Difference; Stability Polynomial