A class of numerical methods for the solution of fourth-order nonlinear ordinary differential equations on a graded mesh with boundary conditions of first kind. Issue 5 (3rd September 2019)

• Record Type: Journal Article
• Authors: Mohanty, R. K.; Hasan Sarwer, Md
• Is Part Of: International journal for computational methods in engineering science and mechanics. Volume 20:Issue 5(2019)
• Page Start: 434
• Page End: 450
• Publication Date: 2019-09-03
• Subjects: Fourth order nonlinear boundary value problems -- boundary conditions of first kind -- graded mesh -- nonlinear biharmonic equation -- fourth-order singular boundary value problems; Engineering -- Data processing -- Periodicals; Engineering mathematics -- Periodicals; Computer-aided engineering -- Periodicals; 620.00420285
• DOI: 10.1080/15502287.2019.1600072
• Languages: English
• ISSNs: 1550-2287

Abstract

Abstract: We propose difference schemes of order 2 and 3 on a graded mesh for fourth-order nonlinear ordinary differential equations (ODEs). The values of u and ( du/dx ) are prescribed at two boundary points. Our methods involve only 3-grid points. A graded mesh is generated by introducing a mesh ratio parameter σ . Numerical values of ( du/dx ) are obtained as a by-product of the proposed methods. The stability and convergence analysis are discussed in brief. The modified version of the method works well for singular problems. We have tested our methods on seven benchmark problems to demonstrate the usefulness of the proposed methods.