Highly Accurate Method for Boundary Value Problems with Robin Boundary Conditions

Abstract The main aim of the current paper is to construct a numerical algorithm for solutions second-order linear and nonlinear differential equations subject Robin boundary conditions. A basis function in terms shifted Chebyshev polynomials first kind that satisfy homogeneous conditions constructed. It has established operational matrices derivatives constructed polynomials. obtained are spectral consequences application collocation method. This method converts problem governed by their into systems or algebraic equations, which can be solved any convenient solver. theoretical convergence error estimates discussed. Finally, we support presented study presenting seven examples ensure accuracy, efficiency, applicability algorithm. results compared with exact from other methods. produces highly accurate agreement between approximate solutions, displayed tables figures.