Global, rigorous and realistic bounds for the solution of dissipative differential equations. I: Theory (Q1332684)
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scientific article; zbMATH DE number 627655
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| English | Global, rigorous and realistic bounds for the solution of dissipative differential equations. I: Theory |
scientific article; zbMATH DE number 627655 |
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Global, rigorous and realistic bounds for the solution of dissipative differential equations. I: Theory (English)
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1 September 1994
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The paper deals with global, rigorous and realistic bounds for the solutions of initial value problem for dissipative differential equations. The authors use one-sided Lipschitz conditions to obtain the local and global errors. A new existence theorem is proved giving conditions under which an initial value problem has a solution that remains close to a given approximation. By methods of interval analysis, logarithmic norms and differential inequalities a set of sufficient conditions is presented that give global bounds for all times.
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error bounds
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dissipative differential equations
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interval analysis
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logarithmic norms
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differential inequalities
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