Application of JMN Approximants to Numerical Initial-value Problems in Linear Differential-algebraic Systems

For f: 0,) R, the J_MN approximant of f(t) is where M and N are non-negative integers and ß_k, _i,K_iare defined constants. Under appropriate conditions on f andprovided Re(_i) > 0 The approximants are the bases of recursions for numerical initial-valueproblems in linear differential-algebraic systems with constantcoefficients. The recursions are stable when N M N–2.Each step of a recursion involves mainly the solution of N/2uncoupled algebraic systems.