Legendre spectral method for the fractional Bratu problem
Harendra Singh, Fahimeh Akhavan Ghassabzadeh, Emran Tohidi, Carlo Cattani
Abstract
In this paper, the Legendre spectral collocation method (LSCM) is applied for the solution of the fractional Bratu's equation. It shows the high accuracy and low computational cost of the LSCM compared with some other numerical methods. The fractional Bratu differential equation is transformed into a nonlinear system of algebraic equations for the unknown Legendre coefficients and solved with some spectral collocation methods. Some illustrative examples are also given to show the validity and applicability of this method, and the obtained results are compared with the existing studies to highlight its high efficiency and neglectable error.
Topics & Concepts
Legendre polynomialsMathematicsAlgebraic equationCollocation (remote sensing)Associated Legendre polynomialsSpectral methodApplied mathematicsCollocation methodLegendre functionMathematical analysisNonlinear systemDifferential equationOrdinary differential equationOrthogonal polynomialsComputer scienceGegenbauer polynomialsMachine learningPhysicsQuantum mechanicsClassical orthogonal polynomialsFractional Differential Equations SolutionsNonlinear Waves and SolitonsIterative Methods for Nonlinear Equations