Solutions of inhomogeneous diffusion equation by the method of characteristics

Gunawan Nugroho*, Nur Laila Hamidah

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review


This work examines the diffusion equation in curvilinear coordinates by using the method of characteristics. The method is commonly applied to solve first order partial differential equations. Applying the method to the diffusion equation, the main difficulty is when the general case is considered i.e., produces variable coefficients. The method utilizes the separation of order in order to solve the problem. The resulted ODEs in the main equation and characteristic variables are performed by the implementation of the general Riccati equation. The procedure is then repeated sequentially to reach the final solutions for concentration distributions.

Original languageEnglish
Title of host publicationLithium-Ion Batteries
Subtitle of host publicationProperties, Advantages and Limitations
PublisherNova Science Publishers, Inc.
Number of pages20
ISBN (Electronic)9781536168464
ISBN (Print)9781536168457
Publication statusPublished - 1 Jan 2020


  • Analytical solutions
  • Curvilinear coordinates
  • Diffusion equation
  • Method of characteristics
  • Reduction of PDEs


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