DAJANA CONTE, RAFFAELE D’AMBROSIO and BEATRICE PATERNOSTER

Construction of diagonally implicit almost collocation methods for Volterra Integral Equations

Pages: 125-146
Received: 1 April 2010   
Accepted: 18 May 2010
Mathematics Subject Classification (2000): 65R20.

Keywords: Numerical methods for Volterra Integral Equations, Two–step collocation methods, Two–step Runge–Kutta methods, Diagonally–implicit methods.

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Abstract: We describe a modification of two-step collocation methods for the numerical solution of Volterra Integral Equations, with particular attention to the construction of efficient and highly stable methods. We present a constructive technique to obtain coefficient matrices having an estabilished structure, e.g. lower triangular or diagonal, and show examples of A-stable methods.