Daba Imiru Takele, Duressa Gemechis File
Department of Mathematics, Dilla university, Dilla, SNNP, P.O. Box 419, Ethiopia.
Department of Mathematics, Jimma university, Jimma, Oromia, P.O. Box 378, Ethiopia.
Heliyon. 2022 Sep 26;8(9):e10742. doi: 10.1016/j.heliyon.2022.e10742. eCollection 2022 Sep.
This paper deals with the computational method for a class of second-order singularly perturbed parabolic differential equations with discontinuous coefficients involving large negative shift. The formulated method comprises the implicit Euler and the cubic-spline in compression methods for time and spatial dimensions, respectively. Intensive numerical experimentation has been done on some model examples and the results are tabulated. The results depict that the present method is more accurate than some methods existing in the literature. Further, the layer behavior of the solutions is presented using graphs and observed to agree with the existing theories. Finally, error analysis of the scheme is done and observed that the proposed method is parameter uniform convergent with the order of convergence .
本文研究了一类具有大负位移且系数间断的二阶奇异摄动抛物型微分方程的计算方法。所提出的方法分别在时间维和空间维上采用隐式欧拉方法和三次样条压缩方法。针对一些模型实例进行了大量数值实验，并将结果制成表格。结果表明，本方法比文献中现有的一些方法更精确。此外，利用图形展示了解的层行为，并观察到其与现有理论相符。最后，对该格式进行了误差分析，发现所提出的方法是参数一致收敛的，收敛阶为 。
