http://fiscomp.if.ufrgs.br/index.php?action=history&feed=atom&title=Lax-Wendroff_de_dois_passos 2026-04-07T17:09:52Z Histórico de revisões para esta página neste wiki MediaWiki 1.39.4 http://fiscomp.if.ufrgs.br/index.php?title=Lax-Wendroff_de_dois_passos&diff=1996&oldid=prev 2018-01-24T17:49:56Z

<p>Criou página com &#039;&lt;source lang=&quot;c&quot;&gt; #include&lt;stdio.h&gt; #include&lt;math.h&gt; #include&lt;string.h&gt; #include&lt;stdlib.h&gt; void atualizar_onda(double u_new[],double u_now[],double u_old[],int jmax,double k...&#039;</p> <p><b>Página nova</b></p><div>&lt;source lang=&quot;c&quot;&gt;<br /> #include&lt;stdio.h&gt;<br /> #include&lt;math.h&gt;<br /> #include&lt;string.h&gt;<br /> #include&lt;stdlib.h&gt;<br /> <br /> <br /> void atualizar_onda(double u_new[],double u_now[],double u_old[],int jmax,double k);<br /> <br /> void main()<br /> {<br /> <br /> FILE *arq;<br /> arq = fopen(&quot;laxw.txt&quot;, &quot;w+&quot;);<br /> <br /> int tmax,i,j,jmax;<br /> <br /> //tamanho da corda: jmax-1<br /> jmax = 50;<br /> <br /> //u: posicao da corda<br /> /* u_old em t-1 */<br /> /* u_now em t */<br /> /* u_new em t+1 */<br /> //k = dt/dx<br /> double u_new[jmax],t,u_old[jmax],u_now[jmax],k,erro;<br /> <br /> //tmax: tempo final<br /> tmax = 100;<br /> k = 0.2;<br /> <br /> <br /> //condição inicial<br /> for (j = 0 ; j &lt; jmax ; j++)<br /> {<br /> u_now[j] = sin(M_PI*j/(jmax - 1));<br /> }<br /> <br /> //condição de contorno<br /> u_old[0] = 0;<br /> u_old[jmax-1] = 0;<br /> <br /> <br /> u_new[0] = 0;<br /> u_new[jmax-1] = 0;<br /> <br /> //cálculo de u para t=-dt, utilizando o método de leapfrog - aqui usamos que du/dt = 0 em t=0<br /> for (j = 1; j&lt; jmax-1 ; j++)<br /> {<br /> u_old[j] = u_now[j] + 0.5 * pow(k,2) * (u_now[j+1] - 2 * u_now[j] + u_now[j-1]);<br /> <br /> }<br /> <br /> <br /> //atualização da onda<br /> for(t = 0 ; t &lt; tmax ; t+=k)<br /> {<br /> <br /> atualizar_onda(u_new,u_now,u_old,jmax,k);<br /> <br /> memcpy(u_old,u_now, sizeof(double)*jmax);<br /> memcpy(u_now,u_new, sizeof(double)*jmax);<br /> }<br /> <br /> //onda no tempo t=tmax<br /> for(j=0; j&lt;jmax; j++)<br /> {<br /> fprintf(arq,&quot;%d %lf\n&quot;, j, u_new[j]);<br /> }<br /> <br /> <br /> fclose(arq);<br /> <br /> }<br /> <br /> <br /> void atualizar_onda(double u_new_[],double u_now_[],double u_old_[],int jmax,double k)<br /> {<br /> int j;<br /> <br /> //para j=1 e j=jmax-2 (penultimas posicoes), necessitamos de u em x=-1 e x=jmax, respectivamente, sendo que essas posicoes ficam fora do vetor (vai de 0 a jmax-1). Aqui, foi feito u(x=-1)=-u(x=1) e u(x=jmax)=-u(x=jmax-2)<br /> j=1;<br /> <br /> u_new_[j] = 2 * u_now_[j] - u_old_[j] + 0.5 * pow(k,2) * (0.5 * u_old_[j+2] - u_old_[j+1] + u_old_[j] - u_old_[j-1] - 0.5 * u_old_[j] + u_now_[j+1] - 2 * u_now_[j] + u_now_[j-1]);<br /> <br /> for(j = 2 ; j &lt; jmax-2 ; j++)<br /> {<br /> u_new_[j] = 2 * u_now_[j] - u_old_[j] + 0.5 * pow(k,2) * (0.5 * u_old_[j+2] - u_old_[j+1] + u_old_[j] - u_old_[j-1] + 0.5 * u_old_[j-2] + u_now_[j+1] - 2 * u_now_[j] + u_now_[j-1]);<br /> }<br /> <br /> j=jmax-2;<br /> u_new_[j] = 2 * u_now_[j] - u_old_[j] + 0.5 * pow(k,2) * (-0.5 * u_old_[j] - u_old_[j+1] + u_old_[j] - u_old_[j-1] + 0.5 * u_old_[j-2] + u_now_[j+1] - 2 * u_now_[j] + u_now_[j-1]);<br /> <br /> <br /> <br /> }<br /> <br /> &lt;/source&gt;</div>

Rodrigozferreira