In this paper, an adaptive grid method is proposed to solve onedimensional unsteady singularly perturbed Burger-Huxley equation with appropriate initial and boundary conditions. Firstly, we use the classical backward-Euler scheme on a uniform mesh to approximate time derivative. The resulting nonlinear singularly perturbed semi-discrete problem is linearized by using Newton-Raphson-Kantorovich approximation method which is quadratically convergent. Then, an upwind finite difference scheme on an adaptive nonuniform grid is used for space derivative. The nonuniform grid is generated by equidistribution of a positive monitor function, which is similar to the arclength function. It is shown that the presented adaptive grid method is first order uniform convergent in the time and spatial directions, respectively. Finally, numerical results are given to validate the theoretical results.

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Electrocardiogram (ECG) signals are crucial for determining the health status of the human heart. A clean ECG signal is critical in analysis and diagnosis of heart diseases. However, ECG signals are often contaminated by motion artifact noise in the non-contact ECG monitoring systems. In this paper, an ECG motion artifact removal approach based on empirical wavelet transform (EWT) and wavelet thresholding (WT) is proposed. This method consists of five steps, namely, spectrum preprocessing, spectrum segmentation, EWT decomposition, wavelet threshold denoising, and EWT reconstruction. The proposed approach was used to process real ECG signals collected by the non-contact ECG monitoring equipment. The results of quantitative study and analysis indicate that this approach produces a better performance in terms of restorage of QRS complexes of the original ECG with reduced distortion, retaining useful information in ECG signals, and improvement of the signal to noise ratio (SNR) value of the signal. The output results of the practical ECG signal test show that motion artifact in the real recorded ECG is effectively filtered out. The proposed method is feasible for reducing motion artifacts from ECG signals, whether from simulation ECG signals or practical non-contact ECG monitoring systems.

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