Highly Efficient Method for Solving Parabolic PDE with Nonlocal Boundary Conditions
Mohamed El‐Gamel, Galal I. El–Baghdady, Mahmoud Abd El-Hady
Abstract
In this work, a highly efficient algorithm is developed for solving the parabolic partial differential equation (PDE) with the nonlocal condition. For this purpose, we employ orthogonal Chelyshkov polynomials as the basis. The convergence analysis of the proposed scheme is derived. Numerical experiments are carried out to explain the efficiency and precision of the proposed scheme. Furthermore, the reliability of the scheme is verified by comparisons with assured existing methods.
Topics & Concepts
Convergence (economics)Partial differential equationScheme (mathematics)MathematicsParabolic partial differential equationReliability (semiconductor)Boundary value problemApplied mathematicsWork (physics)Basis (linear algebra)Mathematical analysisMathematical optimizationGeometryPhysicsEconomic growthThermodynamicsQuantum mechanicsEconomicsPower (physics)Differential Equations and Boundary ProblemsDifferential Equations and Numerical MethodsNumerical methods in inverse problems