Solving heat equation with exponential nonlinearity by Banach contraction method

Raham, Rusul K.; Mamoon, Mustafa

doi:10.47974/JIM-2301

Open Access Research Article

Solving heat equation with exponential nonlinearity by Banach contraction method

^*Rusul K. RahamCorresponding authorrosolkrh23@mtu.edu.iqDepartment of Tourism Management TechnologiesTechnical College of ManagementBaghdad, Iraq0009-0002-2867-7593View full profile → , Mustafa MamoonMUSTAFAMAMOON@mtu.edu.iqDepartment of Information Technology ManagementTechnical College of ManagementBaghdad, Iraq0009-0006-5417-6572View full profile →

* Corresponding author · click or hover a name for details

pp. 1197–1204Vol. 29Issue 5-AMay 2026DOI: 10.47974/JIM-2301XML

Received:: 01 May 2025
Published Online:: 27 Jun 2026
Article type:: Research Article
Language:: EN
Article no.:: JIM-2301
Pages:: 1197–1204

Abstract

This paper examines the Banach Contraction Method (BCM) for solving the heat equation with an exponential nonlinearity. In fact, the (BCM) has been tested via illustrative examples. When applying the BCM, we achieved effective and efficient results by comparing them with those obtained using Adomian decomposition methods. The BCM does not require a restrictive assumption about the nonlinear term, unlike other known methods. The results are also illustrated with tables and figures. All calculations are obtained by Mathematica® 10 program.

Keywords

Nonlinear heat equation Banach contraction method Exponential nonlinearity Numerical solution Absolute error low Mathematica® 10 program

Subject Classifications

Primary 35QxxSecondary 35Q79

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