A Computational Approach for the Calculation of Temperature Distribution in Casting-Mould Heterogeneous System with...

Area of Science:

• Applied Mathematics
• Fractal Calculus
• Nonlinear Dynamics

Background:

• Casting-mould systems involve complex heterogeneous interactions.
• Integer and fractional-order partial differential equations describe these systems.
• Approximate solutions are crucial for analyzing complex physical phenomena.

Purpose of the Study:

• To investigate an approximate solution for casting-mould heterogeneous systems using the Caputo derivative.
• To apply the Yang transform homotopy perturbation method (YT-HPM) for temperature distribution analysis.
• To demonstrate the efficacy of YT-HPM for fractional-order differential equations.

Main Methods:

• The Yang transform homotopy perturbation method (YT-HPM) is employed.
• This method combines the Yang transform (YT) and the homotopy perturbation method (HPM) with He's polynomials.
• The approach is applied to solve fractional-order partial differential equations.

Main Results:

• The YT-HPM provides an effective approximate solution for the temperature distribution in casting-mould heterogeneous systems.
• The method successfully handles both integer and fractional-order differential equations within the system.
• Demonstrated superiority through illustrative examples, showing minimal computational effort.

Conclusions:

• The YT-HPM is a powerful and robust technique for nonlinear problems in fractal calculus.
• This method offers a significant advancement in the functional studies of heterogeneous systems.
• The approach minimizes computational complexity without requiring restrictive assumptions.