Interval Analytic Method in Existence Result for Hyperbolic Partial Differential Equation

Peter O. Arawomo^{*}

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References

[1] Lakshmikantham, V. and Pandit, S.G. (1985) The Method of Upper and Lower Solution and Hyperbolic Partial Differential Equations. Journal of Mathematical Analysis and Applications, 105, 466-477.

http://dx.doi.org/10.1016/0022-247X(85)90062-9

[2] Moore, R.E. (1979) Methods and Application of Interval Analysis. SIAM (Studies in Applied and Numerical Mathematics), Philadelphia. http://dx.doi.org/10.1137/1.9781611970906

[3] Arawomo, P.O. and Akinyele, O. (2002) An Interval Analytic Method in Constructive Existence Result for Initial Value Problems. Dynamic Systems and Applications, 11, 545-556.

[4] Chan, C.Y. and Vatsala, A.S. (1990) Method of Upper and Lower Solution and Interval Method for Semilinear Euler-Pision-Darboux Equations. Journal of Mathematical Analysis and Applications, 150, 378-381.

http://dx.doi.org/10.1016/0022-247X(90)90110-2

[5] Lakshmikantham, V. and Swansundaran, S. (1987) Interval Method for 1st Order Differential Equations. Applied Mathematics and Computation, 23, 1-5. http://dx.doi.org/10.1016/0096-3003(87)90052-X

[6] Moore, R.E. (1984) Upper and Lower Bounds on Solutions of Differential, Integral Equations without Using Monotonicity, Convexity or Maximum Principle., In: Vichnevetsky, R. and Stepheman, R., Eds., Advances in Computer Methods for Partial Differential Equations, IMACS, 458-461.

[7] Moore, R.E. (1984) A Survey of Interval Methods for Differential Equations. Proceedings of 23rd Conference on Decision and Control, Las Vegas, 12-14 December 1984, 1529-1535.

[8] Walter, W. (1970) Differential and Integral Inequalities. Springer-Verlag, Berlin, Heidelberg.

http://dx.doi.org/10.1007/978-3-642-86405-6

[9] Caprani, O. and Madsen, K. (1975) Contraction Mappings in Interval Analysis. BIT Numerical Mathematics, 15, 362-366. http://dx.doi.org/10.1007/BF01931673

[10] Moore, R.E. (1977) A Test for Existence of Solution to Nonlinear Systems. SIAM Journal on Numerical Analysis, 14, 611-615.

[11] Moore, R.E. (1978) Bounding Sets in Function Spaces with Application to Nonlinear Operator Equations. SIAM Review, 20, 492-512.

[12] Rall, L.B. (1983) Mean-Value and Taylor Forms in Interval Analysis. SIAM Journal on Mathematical Analysis, 14, 223-238.

[13] Rall, L.B. (1982) Integration of Interval Functions II, the Finite Case. SIAM Journal on Mathematical Analysis, 13, 690-698.