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ABSTRACT
A search for new integration formulas for finding improved solutions to singular/discontinuous/stiff initial value problems in ordinary differential equations is carried out. Families of variable order one-step rational integrators are proposed for singular and stiff initial value problems. Methods based on more generalized rational polynomials are constructed. These methods have very high degree of accuracy. In fact their degree of accuracy is of higher order than those of existing schemes of similar nature. They are component wise applicable to systems of ordinary differential equations. The first three families are L-stable while the other two are A-stable.
