Software Systems Scientific Computing

Solving Nonlinear Partial Differential Equations with Maple by Inna Shingareva, Carlos Lizárraga-Celaya (auth.)

Posted On March 24, 2017 at 12:47 am by / Comments Off on Solving Nonlinear Partial Differential Equations with Maple by Inna Shingareva, Carlos Lizárraga-Celaya (auth.)

By Inna Shingareva, Carlos Lizárraga-Celaya (auth.)

The emphasis of this paintings is on developing forms of suggestions (exact, approximate analytical, numerical, graphical) of various nonlinear PDEs thoroughly, simply, and quick. The reader can examine a wide selection of options and remedy a variety of nonlinear PDEs incorporated and lots of different differential equations, simplifying and reworking the equations and recommendations, arbitrary services and parameters, offered within the book). various comparisons and relationships among numerous kinds of ideas, various tools and methods are supplied, the implications received in Maple and Mathematica, allows a deeper knowing of the subject

Show description

Read Online or Download Solving Nonlinear Partial Differential Equations with Maple and Mathematica PDF

Best software: systems: scientific computing books

Maple Syrup Urine Disease - A Medical Dictionary, Bibliography, and Annotated Research Guide to Internet References

This can be a 3-in-1 reference booklet. It provides a whole clinical dictionary masking 1000s of phrases and expressions in terms of maple syrup urine sickness. It additionally supplies wide lists of bibliographic citations. eventually, it presents details to clients on the way to replace their wisdom utilizing a number of web assets.

Maple V: Learning Guide

Maple V arithmetic studying consultant is the totally revised introductory documentation for Maple V unlock five. It exhibits the way to use Maple V as a calculator with immediate entry to 1000's of high-level math exercises and as a programming language for extra hard or really good initiatives. issues comprise the elemental information forms and statements within the Maple V language.

Kalman Filtering: Theory and Practice Using MATLAB®, Third Edition

This e-book offers readers with an effective advent to the theoretical and sensible facets of Kalman filtering. it's been up to date with the most recent advancements within the implementation and alertness of Kalman filtering, together with variations for nonlinear filtering, extra strong smoothing tools, and constructing purposes in navigation.

Theory of Lift: Introductory Computational Aerodynamics in MATLAB®/OCTAVE

Ranging from a easy wisdom of arithmetic and mechanics won in average origin periods, conception of carry: Introductory Computational Aerodynamics in MATLAB/Octave takes the reader conceptually via from the basic mechanics of raise  to the level of truly having the ability to make useful calculations and predictions of the coefficient of carry for practical wing profile and planform geometries.

Additional resources for Solving Nonlinear Partial Differential Equations with Maple and Mathematica

Example text

Applying the Maple predefined functions pdsolve with option HINT=strip, dsolve, and charstrip, verify that the solutions (Sol1, Sol2), obtained by the method of characteristics read in the Maple notation: 24 Introduction Sol1 := {u ( s) = C2 , x ( s) = C2 s + C1 , y ( s) = − s + C3 } Sol2 := ux 2 + uy = 0 &where [{{u ( s) = − C3 s + C2 , x ( s) = 2 C4 s + C1 , y ( s) = s + C5 , p 1 ( s) = C4 , p 2 ( s) = C3 }} , { p 1 = ux , p 2 = uy }] Maple : with(PDEtools); declare(u(x,y)); PDE1:=u(x,y)*diff(u(x,y),x)=diff(u(x,y),y); PDE2:=diff(u(x,y),x)^2+diff(u(x,y),y)=0; sysCh:=charstrip(PDE1,u(x,y)); funcs:=indets(sysCh,Function); Sol1:=dsolve(sysCh,funcs,explicit); Sol2:=pdsolve(PDE2,HINT=strip); For the given equation PDE1, we first obtain the characteristic system (depending on a parameter s) via charstrip, and solve this system via dsolve to obtain the solution Sol1 in the parametric form.

3 KdV equation. Nonlinear heat equation. Nonlinear telegraph system. Translation transformations. Let us consider the KdV equation (Eq11), the nonlinear heat equation (Eq21), and the nonlinear telegraph system (sys1): ut +uux +uxxx =0, ut − F (u(x, t))ux vt −F (u(x, t))ux −G(u(x, t))=0, x =0, ut −vx =0, where {x ∈ R, t ≥ 0}, (x, t) are the independent variables, (u, v) are the dependent variables, and F (u), G(u) are arbitrary functions. , the resulting equations and system take the form (Eq12, Eq22, sys2): uT +u(X,T )uX +uXXX , uT − F (u(X,T ))uX vT −F u(X,T ) uX −G(u(X,T ))=0, X =0, uT −vX =0.

Solution Sol20 is equivalent to pdsolve(Eq2,build). With the aid of the predefined function TWSolutions we can find different types of traveling wave solutions (of nonlinear PDEs and their systems) according to a list of functions Fs (instead of the tanh function, by default). The algorithm is based on the tanh-function method and its various extensions (see Sect. 2). , all particular cases of more general solutions being constructed), we can obtain numerous traveling wave solutions (Sol21). For example, specifying the cot and tan functions and other options, we can obtain various traveling wave solutions.

Download PDF sample

Rated 4.93 of 5 – based on 30 votes