Unconditionally stable C¹-cubic spline collocation method for solving parabolic equations

High-order compact solution of the one-dimensional heat and advection–diffusion equations

“…We use the compact finite difference approximation of fourth-order for discretizing spatial derivatives of advection-diffusion equation and the cubic C 1 -spline collocation method for the resulting linear system of ordinary differential equations. Cubic C 1 -spline collocation is an A-stable method and has fourth-order accuracy [45,46]. Another advantage of the proposed method is the unconditional stability which will be proved in this paper.…”

A Non-polynomial Spline Method for Solving the One-Dimensional Heat Equation

“…Recently, an unconditionally stable C 1 -cubic spline collocation method for Eq. (1) was proposed in [5] with the truncation error being O(k 4 + h 2 ).…”

Hybrid Spline Difference Method for Steady-State Heat Conduction

“…In terms of the earlydeveloped cubic spline (Wang and Kahawita [12]), if uniform grids are taken, then the first derivative and second derivative have fourth-order and second-order accuracy, respectively, hence numerical solution of the spline has been widely applied. There is much recent research based on the spline theory, such as the high-precision C 1 -cubic spline collocation method [13], the quartic spline method [14], the residual error-correction method [15], and the parameter spline method [16,17].…”