A fourth-order exponential time differencing scheme with real and distinct poles rational approximation for solving non-linear reaction-diffusion systems. [PDF]
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Aquila Optimization-Assisted Artificial Neural Network for Classification Problems. [PDF]
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Risk factors for recurrent falls in midlife: a prospective cohort study using data from the Health and Employment After Fifty (HEAF) study. [PDF]
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Mathematical Methods in the Applied Sciences, 2019In this paper, we deal with the backward problem of determining initial condition for Rayleigh‐Stokes where the data are given at a fixed time. The problem has many applications in some non‐Newtonian fluids. We give some regularity properties of the solution to backward problem.
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Mathematical Methods in the Applied Sciences, 2019In this paper, we consider the nonlinear biharmonic equation. The problem is ill‐posed in the sense of Hadamard. To obtain a stable numerical solution, we consider a regularization method. We show rigourously, with error estimates provided, that the corresponding regularized solutions converge to the true solution strongly in uniformly with respect ...
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Error Bounds in the Final Value Problem for the Heat Equation
SIAM Journal on Mathematical Analysis, 1976Consider the following problem. Given the positive constants $\delta $, M, T and $f(x)$ in $L^2 (\Omega )$, find all solutions of $u_t = \Delta u$ in $\Omega \times (0,T]$, $u = 0$ on $\partial \Omega \times (0,T]$, such that $\| {u( \cdot ,T) - f} \|_{L^2 } \leqq \delta $, $\| {u( \cdot ,0) - f} \|_{L^2 } \leqq M$.
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