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systems; sufficient conditions for convergence; Gronwall inequality; error bound

References:

[1] Babuška I., Práger M., Vitásek E.: **Numerical processes in differential equations**. Praha 1966. MR 0223101

[2] Hartman P.: **Ordinary differential equations**. New York: John Wiley and Sons 1964. MR 0171038 | Zbl 0125.32102

[3] Hayoshi K.: **On stability of numerical solutions of a differential system by one-step methods**. TRU Mathematics 5, 67-83 (1969). MR 0269123

[4] Henrici P.: **Discrete variable methods in ordinary differential equations**. New York: John Wiley and Sons 1968. MR 0135729

[5] Ohashi T.: **On the conditions for convergence of one-step methods for ordinary differential equations**. TRU Mathematics 6, 59-62 (1970). MR 0331791 | Zbl 0252.65054

[6] Squier D. P.: **One-step methods for ordinary differential equations**. Numer. Math. 13, 176-179 (1969). DOI 10.1007/BF02163235 | MR 0247773 | Zbl 0182.21901