Summary
For certain nonlinear two-point boundary value problems of the fourth order an estimation theory is developed which yields simultaneous estimates of the solution and its second derivative. Methods for computing numerical error bounds for approximate solutions are described and tested. The theory provides also uniqueness and existence statements. The results can be applied to many problems for which a corresponding theory on two-sided bounds is not suitable.
Similar content being viewed by others
References
Ehlich, H., Zeller, K.: Schwankung von Polynomen zwischen Gitterpunkten. Math. Z.86, 41–44 (1964)
Ruttmann, B.: Untersuchungen zur Fehlerabschätzung von polynomialen Näherungslösungen bei Randwertaufgaben gewöhnlicher Differentialgleichungen. Diss. Univ. Köln, 1982
Schröder, J.: Operator Inequalities. New York: Academic Press 1980
Schröder, J.: Fourth order two-point boundary value problems; estimates by two-sided bounds. Nonlinear Analysis (in press)
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Schröder, J. Numerical error bounds for fourth order boundary value problems, simultaneous estimation ofu(x) andu″(x) . Numer. Math. 44, 233–245 (1984). https://doi.org/10.1007/BF01410108
Issue Date:
DOI: https://doi.org/10.1007/BF01410108