Third derivative hybrid block integrator for solution of stiff systems of initial value problems
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A new third derivative hybrid block method is presented for the solution of first order stiff systems of initial value problems. The main method and additional methods are obtained from the same continuous scheme derived via interpolation and collocation procedures using power series as the basis function. The continuous representation of the scheme permits us to evaluate at both grid and off-grid points. The stability properties of the method is discussed. The block method is applied simultaneously to generate the numerical solutions of (1) over non-overlapping intervals. Numerical results obtained using the proposed third derivative hybrid method in block form reveal that it compares favorably well with existing methods in the literature.
Block hybrid method · Off-step points · Collocation and interpolation · Stability