An Accurate Analytical Solution to Troesch’s Problem Through Lower and Upper Envelope Techniques

Abstract

We consider a novel approach to providing highly accurate analytic solutions to non-classical, non-linear problems. This approach is then implemented to the highly sensitive Troesch-problem, which possesses a boundary layer at the right-end: we determine an upper and lower envelope solution, and compare the average to existing numerical results. Computer simulations show that the proposed analytic solution is highly accurate when compared to the existing benchmark. This confirms that the proposed approach to deal with such non-linear problems can be used to treat similar non-classical boundary-value problems.

Keywords

• Primary 34B15
• Secondary 34L30
• 34B60