Core Concepts
Proposal of a mesh-free method for solving a nonlinear time-fractional biharmonic problem using weighted b-splines.
Abstract
The article introduces a fully-discrete scheme for solving a nonlinear time-fractional biharmonic problem using weighted b-splines. It converts the problem into an equivalent system, discretizes spatially and temporally, and combines computational benefits of b-splines and mesh-based elements. The proposed method provides smooth approximations with few parameters, enforces essential boundary conditions accurately, and exhibits superior convergence rates compared to previous schemes. The paper includes theoretical findings supported by numerical experiments validating the proposed method's advantages.
Stats
Dαt u + ∆2u - ∆u = f(u) in Σ,
Dαt u(x,t) ∶= 1/Γ(1 - α) ∫0(t - s)^-α ∂u(x,s)/∂s ds for 0 < α < 1.
Authors considered various PDEs including linear time-fractional biharmonic problems.
Proposed scheme based on L2-1σ approximation and weighted b-splines.
Error estimates derived for the fully-discrete scheme.