Developments in numerical methods for problems governed by nonlinear partial differential equations underpin simulations with sound arguments in diverse areas of science and engineering. In this paper, we explore the regularization method for the coupled elliptic sine-Gordon equations along with Cauchy data.The system of equations originates from the static case of the coupled hyperbolic sine-Gordon equations modeling the coupled Josephson junctions in superconductivity, and so far it addresses the Josephson πjunctions. In general, the Cauchy problem is not well-posed, and herein the Hadamard-instability occurs drastically. Generalizing the kernel-based regularization method, we propose a stable approximate solution. Confirmed by the error estimate, this solution strongly converges to the exact solution in L 2 -norm.The main concern of this paper is also with the way to compute the regularized solution formed by an alike integral equation. We employ the proposed techniques that successfully approximated the highly oscillatory integral, and apply the Picard-like iteration to organize an efficient and reliable tool of computations.The results are viewed as the improvement as well as the generalization of many previous works. The paper is also accompanied by a numerical example that demonstrates the potential of this idea.

Species identification is beneficial for many aspects of life and scientific research, but the experiment method based on biochemistry may be subjective and inaccuracy in several cases. In order to solve this problem, searching genes in the database is one of the most effective and accurate methods for identification of the Bacillus. However, in the case of the incomplete database, the searching algorithm cannot identify genes which are not in the database. Thus, in this research, we proposed a novel feature to identify the Bacillus based on their codon usage bias, called relative synonymous codon pair usage (RSCPU). We extracted this feature from genes collected from National Center for Biotechnology Information (NCBI) website; then, K -means clustering and Support Vector Machine were applied to classify genes vectored. Finally, we used this method for Bacillus identification and obtained a result that our accuracy is about 3 times (2.93) higher than past research [1].