matlab代写代考

clear all; close all; Delta_t=1.0e-4; %Delta_t=1.0e-5; %Delta_t=1.0e-6; %Delta_t=1.0e-7; t=0:Delta_t:10.0; % preallocating memory & set elements to zero %x=zeros(1,numel(t)); x(1)=0.0; tic % start timer for n=1:length(t)-1 x(n+1)=x(n)+Delta_t*(1-x(n)); end temp=toc; %end timer fprintf(1,’It takes %e seconds to execute the Matlab program\n’,temp);

clear all Npoints=30; alpha = 1; %BC1 y(-1)=alpha beta = 0; %BC2 y'(1)=beta %xpoints=linspace(-1,1,Npoints)’; [xpoints,w,P]=lglnodes(Npoints); xpoints=-xpoints; y = @(x) -(1-16*exp(4)+4*exp(8)-exp(4+4*x)+4*exp(8)*x)./(16*exp(4)); yexact = y(xpoints); n=length(xpoints)-1; %order of polynomial D=DerivMatrix(xpoints,n); D2 = D*D; r = exp(4*xpoints); Amatrix=[D2(2:end-1,2:end);D(end,2:end)]; Cvector=[r(2:end-1);beta]-alpha*[D2(2:end-1,1);D(end,1)]; sol = Amatrix\Cvector; yapprox = [alpha;sol]; hold off plot(xpoints,yapprox,’bo’) hold on plot(xpoints,yexact,’k-‘) xlabel(‘x’);ylabel(‘y’) function D=DerivMatrix(x,n) D=zeros(n+1,n+1); for i=1:n+1 num(i)=1.0;

clear all; close all; Delta_t=0.05; t=0:Delta_t:50; % %Preallocating Memory % x=zeros(length(t),2); x(1,1)=1.0;x(1,2)=0.0; for n=1:length(t)-1 x(n+1,:)=Findxnplus1(Delta_t,x(n,:)); end %Check with Matlab solution [tmat,xmat] = ode23(@Example22p4,[0 50],[1 0]); hold off plot(t,x(:,1),’k-.’,tmat,xmat(:,1),’k-‘); hold on plot(t,x(:,2),’b-.’,tmat,xmat(:,2),’b-‘); legend(‘x_0(t) Crank-Nicolson’,’x_0(t) MATLAB ode23()’,’x_1(t) Crank-Nicolson’,’x_1(t) MATLAB ode23()’); xlabel(‘t’,’Fontsize’,18);ylabel(‘x_i(t)’,’Fontsize’,18); function p=Findxnplus1(Delta_t,xn) eps=1.0; %Just making sure you go through the loop at least once p=xn; %Guess

[Content_Types].xml _rels/.rels matlab/document.xml matlab/output.xml metadata/coreProperties.xml metadata/mwcoreProperties.xml metadata/mwcorePropertiesExtension.xml metadata/mwcorePropertiesReleaseInfo.xml Numerical Integration In this livescript, you will learn how to Apply the Trapezoidal rule and Simpsons’s rule to approximate integrals. Apply Gaussian quadrature to approximate integrals Numerical Integration The main idea behind numerical integration (or quadrature) is to approximate a complicated function at some set of points

[Content_Types].xml _rels/.rels matlab/document.xml matlab/output.xml metadata/coreProperties.xml metadata/mwcoreProperties.xml metadata/mwcorePropertiesExtension.xml metadata/mwcorePropertiesReleaseInfo.xml Runge-Kutta Methods In this livescript, you will learn how To solve initial value problems using Runge-Kutta methods. Previously, we saw that with the explicit Euler method, we saw that the value of x_{n+1} is given by x_{n+1}=x_{n}+\Delta tf(t_{n},x_{n}) However, the only problem with it was that it

clear all tic xmatlab1 = fsolve(@NonlinearExample,[1;1;1]); toc options = optimoptions(@fsolve,’Display’,’iter’,’SpecifyObjectiveGradient’,true); tic [xmatlab2,F,exitflag,output,JAC] = fsolve(@NonlinearExampleWithJacobian,[1;1;1],options); toc x=[1;1;1] [f,J]=NonlinearExampleWithJacobian(x); while max(abs(f)) > 1.0e-8 [L,U]=LUDecomposition(J); R=LowerTriangularSolver(L,-f); diff=UpperTriangularSolver(U,R); x=diff+x [f,J]=NonlinearExampleWithJacobian(x); end function [f,J] = NonlinearExampleWithJacobian(x) f(1) = 3*x(1)+cos(x(2)*x(3))-1/2; f(2) = x(1)^2-81*(x(2)+0.1)^2 +sin(x(3)) + 1.06; f(3)=exp(-x(1)*x(2)) +20*x(3)+(10*pi-3)/3; J(1,1)=3;J(1,2)=-x(3)*sin(x(2)*x(3));J(1,3)=-x(2)*sin(x(2)*x(3)); J(2,1)=2*x(1);J(2,2)=-16.2-162*x(2);J(2,3)=cos(x(3)); J(3,1)=-x(2)*exp(-x(1)*x(2));J(3,2)=-x(1)*exp(-x(1)*x(2));J(3,3)=20; end function f = NonlinearExample(x) f(1) = 3*x(1)+cos(x(2)*x(3))-1/2; f(2) =