Coincidence Best Proximity Point Results via $$ w_{p}$$-Distance with Applications

Saleem, Naeem

doi:10.1007/978-981-16-4896-0_12

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2022

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“…The iterative method presented by Avudai Selvi and Ramanujam [29] can be applied to the problem considered in the paper. The convergence iterates with a suitable initial guess can be studied by the results given in [30][31][32].…”

Section: Introductionmentioning

confidence: 99%

Stable Difference Schemes with Interpolation for Delayed One-Dimensional Transport Equation

2022

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In this article, we consider the one-dimensional transport equation with delay and advanced arguments. A maximum principle is proven for the problem considered. As an application of the maximum principle, the stability of the solution is established. It is also proven that the solution’s discontinuity propagates. Finite difference methods with linear interpolation that are conditionally stable and unconditionally stable are presented. This paper presents applications of unconditionally stable numerical methods to symmetric delay arguments and differential equations with variable delays. As a consequence, the matrices of the difference schemes are asymmetric. An illustration of the unconditional stable method is provided with numerical examples. Solution graphs are drawn for all the problems.

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Section: Introductionmentioning

confidence: 99%