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A high-order exponential integrator for nonlinear parabolic equations with nonsmooth initial data. (English) Zbl 1464.65051

Summary: A variable stepsize exponential multistep integrator, with contour integral approximation of the operator-valued exponential functions, is proposed for solving semilinear parabolic equations with nonsmooth initial data. By this approach, the exponential \(k\)-step method would have \(k^{\text{th}}\)-order convergence in approximating a mild solution, possibly nonsmooth at the initial time. In consistency with the theoretical analysis, a numerical example shows that the method can achieve high-order convergence in the maximum norm for semilinear parabolic equations with discontinuous initial data.

MSC:

65J08 Numerical solutions to abstract evolution equations
35K55 Nonlinear parabolic equations
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