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We consider high order, implicit Runge-Kutta schemes to solve time-dependentstiff PDEs on dynamically adapted grids generated by multiresolution analysisfor unsteady problems disclosing localized fronts. The multiresolution finitevolume scheme yields highly compressed representations within a user-definedaccuracy tolerance, hence strong reductions of computational requirements tosolve large, coupled nonlinear systems of equations. SDIRK and RadauIIARunge-Kutta schemes are implemented with particular interest in those withL-stability properties and accuracy-based time-stepping capabilities. Numericalevidence is provided of the computational efficiency of the numerical strategyto cope with highly unsteady problems modeling various physical scenarios witha broad spectrum of time and space scales.

High order implicit time integration schemes on multiresolution adaptive grids for stiff PDEs