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IMA Journal of Applied Mathematics 1978 22(4):457-465; doi:10.1093/imamat/22.4.457
© 1978 by Institute of Mathematics and its Applications
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Approximate Operators and Dual Extremum Principles for Linear Problems

P. SMITH

Department of Mathematics, The University, Keele, Staffs England

The use of approximate operators in the theory of dual extremum principles is investigated for certain linear problems. If second-order trial functions to certain approximate Lagrangian equations can be found, bounds which are improvements on the dual bounding functions can be constructed. Some simple applications to a partial differential equation and an integral equation are given. It is shown that both upper and lower bounds follow from one trial function.


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