A special class of continuous general linear methods

D.G. Yakubu, A.M. Kwami, M.L. Ahmed
2012 Computational and Applied Mathemathics  
We consider the construction of a class of numerical methods based on the general matrix inverse [14] which provides continuous interpolant for dense approximations (output). Their stability properties are similar to those for Runge-Kutta methods. These methods provide a unifying scope for many families of traditional methods. They are self-starting, to change stepsize during integration is not difficult when using them. We exploited these properties by first obtaining the direct block methods
more » ... ssociated with the continuous schemes and then converting the block methods into uniformly A-stable high order general linear methods that are acceptable for solving stiff initial value problems. However, we will limit our formulation only for the step numbers k = 2, 3, 4. From our preliminary experiments we present some numerical results of some initial value problems in ordinary differential equations illustrating various features of the new class of methods. Mathematical subject classification: 65L05.
doi:10.1590/s1807-03022012000200003 fatcat:zrd52ykdkzet7m6doec5udvoii