CAJ | 학술논문

提出了求解线性奇异摄动滞时微分方程基于指数拟合技术的一致收敛和最佳一致收敛的数值方法,并证明了方法的一致收敛性.利用线性化的思想,并结合Newton-Raphson迭代,构造了求解非线性奇异摄动滞时微分方程相应的一致收敛的算法.数值例子验证上述理论结论的正确性.
제출료구해선성기이섭동체시미분방정기우지수의합기술적일치수렴화최가일치수렴적수치방법,병증명료방법적일치수렴성.이용선성화적사상,병결합Newton-Raphson질대,구조료구해비선성기이섭동체시미분방정상응적일치수렴적산법.수치례자험증상술이론결론적정학성.
Uniformly convergent and optimal uniformly convergent numerical schemes based on the exponential fitting technique were proposed for solving linear singular perturbation problems with after-effect. Corresponding uniformly convergent numerical schemes were constructed by linearization combined with Newton-Raphson iteration for nonlinear problems. Numerical examples were given to confirm the theoretical results.