A class of non-uniform mesh three point arithmetic average discretization for y″ = f( x, y, y′) and the estimates of y

• Published in: Applied mathematics and computation Vol. 183; no. 1; pp. 477 - 485
• Main Author: Mohanty, R.K.
• Format: Journal Article
• Language: English
• Published: New York, NY Elsevier Inc 01.12.2006; Elsevier
• Subjects: Burgers’ equation; Diffusion–convection equation; Estimation; Exact sciences and technology; Mathematical analysis; Mathematics; Non-linear equation; Non-uniform mesh; Numerical analysis; Numerical analysis. Scientific computation; Ordinary differential equations; Partial differential equations; RMS errors; Sciences and techniques of general use; Singular problem; Non-uniform mesh; Burgers’ equation; RMS errors; Non-linear equation; Diffusion–convection equation; Singular problem; Estimation; RMS errors; Error analysis; Differential equation; Convection diffusion equation; RMS error; Boundary condition; Burgers equation; Discretization method; Convergence; Non linear equation; Numerical analysis; Applied mathematics; Non-uniform mesh; Non-linear equation; Singular problem; Diffusion-convection equation; Burgers' equation
• ISSN: 0096-3003; 1873-5649
• DOI: 10.1016/j.amc.2006.05.071

We propose two new non-uniform mesh three point arithmetic average discretization strategy of order two and three, to solve non-linear ordinary differential equation y″ = f( x, y, y′), a < x < b and the estimates of first-order derivative y′, where y = y( x), subject to the essential boundary conditions y( a) = A, y( b) = B. Both methods are compact and directly applicable to singular problems. There is no need to discuss any special scheme for the singular problems. Error analysis of a proposed method is discussed. Numerical experiments are performed to study the convergence behaviors and efficiency of the proposed methods.