The generalized nonlinear Klien-Gordon equation plays an important role in quantum mechanics. In this paper, a new three-time level implicit approach based on cubic trigonometric B-spline is presented for the approximate solution of this equation with Dirichlet boundary conditions. The usual finite difference approach is used to discretize the time derivative while cubic trigonometric B-spline is applied as an interpolating function in the space dimension. Several examples are discussed to exhibit the feasibility and capability of the approach. The absolute errors and L∞ error norms are also computed at different times to assess the performance of the proposed approach and the results were found to be in good agreement with known solutions and with existing schemes in literature.
The tongue and hard palate play an essential role in the production of sound during continuous speech. Appropriate tongue and hard palate contacts will ensure proper sound production. Electropalatography, also known as EPG, is a device that can be used to identify the location of the tongue and hard palate contact. It can also be used by a speech therapist to help patients who have a speech disorder. Among the group with the disease are cleft palate, Down syndrome, glossectomy, and autism patients. Besides identifying the contact location, EPG is a useful medical device that has been continuously developed based on the patient's needs and treatment advancement. This article reviews the technology of electropalatography since the early introduction of the device. It also discusses the development process and the drawbacks of the previous EPG systems, resulting in the EPG's upgraded system and technology. This review suggests additional features that can be useful for the future development of the EPG. The latest technology can be incorporated into the EPG system to provide a more convenient method. There are some elements to be considered in the development of EPG's new technology that were discussed in this study. The elements are essential to provide more convenience for the patient during speech therapy. New technology can accelerate the growth of medical devices, particularly on the development of speech therapy equipment that should be based on the latest technological advancements available. Thus, the advanced EPG system suggested in this article may expand the usage of the EPG and serve as a tool to provide speech therapy treatment services and not limited to monitoring only.