(507) Difference Equations معادلات الفرق - I. Abdel Karim, Abbas (INP, 2024)
The study covers a range of fundamental topics in difference equations and their mathematical applications. It begins with an introduction to linear difference equations with constant coefficients, addressing both homogeneous and non-homogeneous equations with illustrative examples. then explores the use of difference equations in calculating Fibonacci numbers and their algorithmic applications, as well as their use in integrations and the calculation of special functions, such as Chebyshev polynomials and Legendre polynomials. The stability of numerical methods for solving differential equations, including the Euler-Cauchy method and Simpson’s rule, is also discussed. It includes flowcharts for various algorithms and tests for evaluating these methods.