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Solving singularly perturbed Riccati equation with Mathematica
Communications in Numerical Methods in Engineering, 2003AbstractAn exponentially fitted finite‐difference scheme of order one for singularly perturbed Riccati equation has been presented and tested on three problems in this journal (Selvakumar K. Commun. Numer. Meth. Engng 1997; 13: 1–12). This note demonstrates the superiority of Mathematica in solving the same problems.
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On a Class of Singularly Perturbed Parabolic Equations
ZAMM, 2001Summary: A method of matched asymptotic expansions has been used to construct an \(n\)-term uniformly valid approximate solution for an initial-value problem of a linear singularly perturbed parabolic equation exhibiting an internal layer behavior. It is shown that each internal layer function caused by a non-smooth initial data can be described by an \
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Decomposition of linear singularly perturbed functional-differential equations
2021The authors consider the system of functional-differential equations \[ \begin{alignedat}{3} \frac{dx}{dt}&= L_0x_t + L_1(t)x_t + L_2(t) y_t, &\quad x_t(0)&= \varphi(\theta), &\quad &\theta\in [-\Delta,0],\\ \varepsilon\,\frac{dy}{dt}&=L_3(t)y_t + L_4(t)x_t, &\quad y_t(0)&= \psi(\theta), &\quad &\theta\in [-\varepsilon\Delta,0], \end{alignedat ...
Perestyuk, M.O., Cherevko, I.M.
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Applications of IRPSM for Singularly Perturbed and Singularly Perturbed Delay Differential Equations
Abdullah Dawar, Hamid Khanopenaire +1 more source