New Implicit General Linear Method
A New implicit general linear method is designed for the numerical olution of stiff differential Equations. The coefficients matrix is derived from the stability function. The method combines the single-implicitness or diagonal implicitness with property that the first two rows are implicit and third and fourth row are explicit. Also the last row of A and U matrix are identical to the first row of B and V of the partitioned block matrix. The method is almost A stable of order four and it has four stages. This has more advantage than the backward differentiation formula in which no A-stable method can be found with order greater than two. This paper also reviews an algorithm for determining the coefficients matrix from the stability function. It is also shown that the new method is less expensive compared to most existing methods.
Keywords: General Linear Methods, stiff differential equations, singly-Implicit Methods