Explicit stabilized multirate method for stiff differential equations

Stabilized Runge–Kutta methods are especially efficient for the numerical solution of large systems stiff nonlinear differential equations because they fully explicit. For semi-discrete parabolic problems, instance, stabilized overcome stringent stability condition standard without sacrificing explicitness. However, when stiffness is only induced by a few components, as in presence spatially local mesh refinement, their efficiency deteriorates. To remove crippling effect severely components on entire system equations, we derive modified equation, whose solely depends remaining mildly components. By applying to this then devise an explicit multirate Runge–Kutta–Chebyshev (mRKC) method conditions independent Stability mRKC proved model problem, whereas its and usefulness demonstrated through series experiments.