In this Chapter we consider applications of approximate quasi-interpolation to solve initial value problems for classical partial differential equations efficiently and fast. In Sect. 5.1, we use integral representations of solutions to the \(n-\) dimensional heat equations to derive approximate solutions via approximate approximations and tensor product representations. In Sect. 5.2 we derive efficient and fast formulas for the solutions of the Stokes equations. Finally, in Sect. 5.3 we apply our method to uncoupled quasi-static thermoelasticity .

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Approximate Solution of Non-stationary Problems

  • Flavia Lanzara,
  • Vladimir Maz’ya,
  • Gunther Schmidt

摘要

In this Chapter we consider applications of approximate quasi-interpolation to solve initial value problems for classical partial differential equations efficiently and fast. In Sect. 5.1, we use integral representations of solutions to the \(n-\) dimensional heat equations to derive approximate solutions via approximate approximations and tensor product representations. In Sect. 5.2 we derive efficient and fast formulas for the solutions of the Stokes equations. Finally, in Sect. 5.3 we apply our method to uncoupled quasi-static thermoelasticity .