Approximating Higher Order Linear Fredholm Integro-Differential Equations by an Efficient Adomian Decomposition Method

Abstract

This work presents a unique technique for the precise and efficient solution of Linear Fredholm integro-differential equations (LFDEs), the technique is based on the Modification of Adomian Decomposition Method (MADM). The MADM extends the well-known Adomian Decomposition Method (ADM) by integrating novel changes that improve convergence and computing efficiency. The LFDEs are essential for simulating a wide range of phenomena in science and engineering. Because their analytical solutions are frequently difficult to achieve, the development of efficient and trustworthy numerical approaches is required. We present an introduction of the MADM method and its important characteristics emphasizing its capacity to handle a wide range of LFDEs seen in scientific and engineering applications. We demonstrate the method’s usefulness in contrast to the true approach, stressing its computational benefits and precision.

Keywords

• Fredholm Integro
• differential Equations
• Numerical Solutions
• Computational Efficiency

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