The nonexistence of spurious solutions to discrete,two-point boundary value problems |
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Institution: | Centre for Applied Dynamical Systems, Mathematical Analysis and Probability Department of Mathematics, The University of Queensland Brisbane, Queensland 4072, Australia |
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Abstract: | We investigate difference equations which arise as discrete approximations to two-point boundary value problems for systems of second-order, ordinary differential equations. We formulate conditions under which all solutions to the discrete problem satisfy certain a priori bounds which are independent of the step-size. As a result, the nonexistence of spurious solutions are guaranteed. Some existence and convergence theorems for solutions to the discrete problem are also presented. |
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