Closed Form Solutions to Nonlinear Heat Conduction Problems

2012 ◽  
Vol 326-328 ◽  
pp. 115-119
Author(s):  
J. Zabadal ◽  
R. Garcia ◽  
V. Ribeiro ◽  
F. Van Der Laan
Keyword(s):  
Heat Conduction ◽  
Partial Differential Equations ◽  
Closed Form ◽  
Control Systems ◽  
Analytical Method ◽  
Linear Models ◽  
Nonlinear Partial Differential Equations ◽  
Nonlinear Heat Conduction ◽  
Closed Form Solutions ◽  
Standard Techniques

This work presents a new analytical method for solving nonlinear heat conduction problems in arbitrary domains. The method is based on approximate mappings which transforms nonlinear partial differential equations into linear models which can be solved using standard techniques. In order to verify whether the proposed formulation can be employed to conceive new online control systems, numerical results are reported.

scholarly journals On closed-form solutions of some nonlinear partial differential equations

2000 ◽  
Vol 23 (2) ◽  
pp. 81-88 ◽  
Author(s):  
S. S. Okoya
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Wave Equation ◽  
Steady State ◽  
Closed Form ◽  
Nonlinear Wave Equation ◽  
Nonlinear Partial Differential Equations ◽  
Partial Differential ◽  
Closed Form Solutions ◽  
Thermal Explosion Theory

This paper is devoted to closed-form solutions of the partial differential equation:θxx+θyy+δexp(θ)=0, which arises in the steady state thermal explosion theory. We find simple exact solutions of the formθ(x,y)=Φ(F(x)+G(y)), andθ(x,y)=Φ(f(x+y)+g(x-y)). Also, we study the corresponding nonlinear wave equation.

scholarly journals Application of Conformable Sumudu Decomposition Method for Solving Conformable Fractional Coupled Burger’s Equation

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Hassan Eltayeb ◽  
Said Mesloub
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Analytical Method ◽  
Decomposition Method ◽  
Nonlinear Partial Differential Equations ◽  
One Dimensional ◽  
Burger's Equation ◽  
Burger’S Equation ◽  
Sumudu Transform ◽  
Linear And Nonlinear

The conformable double Sumudu decomposition method (CDSDM) is a combination of decomposition method (DM) and a conformable double Sumudu transform. It is an approximate analytical method, which can be used to solve linear and nonlinear partial differential equations. In this work, one-dimensional conformable functional Burger’s equation has been solved by applying conformable double Sumudu decomposition. Two examples are used to illustrate the method.

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